ALISON BOSHOFF: Proof that Jerry and Mick are better friends than ever, especially now he doesn't have to pay her anymore

What a picture of joyous family unity Rolling Stone Mick Jagger and Jerry Hall make.

Together for 23 years — and sharing four grown-up children — both beamed delightedly recently while showing off their latest grandchild with son, James, and daughter Georgia May on Instagram.

The body language of the pair — who split up 24 years ago — speaks volumes. His arm is lovingly draped around his ex's shoulder, while she beams for the camera.

Look closer, and you will see that they are also holding hands.

It's a world away from the time when Jerry — bruised and emotional after Mick impregnated Brazilian model Luciana Morad in 1999 — described him as 'a sick addictive womaniser who made me unhappy'.

Because what was a bitter split has, somehow, become a loving friendship. Mick and Jerry — once riven by arguments over his endless cheating, not to mention protracted wrangling over her financial settlement after their relationship ended — now head the most unlikely of happy families.

'They genuinely do hang out together,' says one friend, adding: 'I have never, ever heard Mick say a negative word about her.'

So content are they in each other's company that I have been told Jerry will be invited to Mick's complex of Balinese style villas in Mustique for as much or as little of the festive season as she wishes.

By tradition, Mick — who has eight children by five women — invites all of his offspring and their families, to join him on the Caribbean island where he has had a home since the 1970s. This year Jerry is very much on the list, too.

The late Princess Margaret sold Mick on the joys of Mustique when they were at a party together.

Today, the ties to the island run deep for the Jaggers, and Jerry has years of happy memories there. Indeed, their son Gabriel met his Swiss socialite wife, Anouk Winzenried, on Mustique where her family also have a place.

It's something of a triumph for Jerry, 67, to be back at the heart of Mick's life. 'They get on brilliantly,' says a long-standing friend. 'Of course, things are better now because she's not asking him for money — and he's not having to give her any.'

A cynical view, perhaps. However it's fair to say that since Jerry's marriage to media titan Rupert Murdoch ended last summer, she and Mick have grown ever closer.

Part of this is undoubtedly down to his support of her after what was a brutal split. Jerry was left reeling when Murdoch ended their six-year marriage by email.

But money, as ever with the famously parsimonious Mick, matters. The fact is that Jerry, once reduced to battling unsuccessfully for her share of the family home in Richmond, South-West London, is now very comfortable.

Her settlement from Murdoch was somewhere between $50 million and $250 million, and she also got an £11 million home in Oxfordshire and a house near Nice.

The £10 million she eventually received from Mick looks like peanuts in comparison.

Jerry has genuinely welcomed Mick's emotional counsel and friendship. For example, after believing the CCTV at her home in the Cotswolds might be sending images back to Murdoch's security detail, Jerry was thrilled when Mick came to the rescue and got his people to 'take care of it'.

I'm told Christmas in the Caribbean with Mick is far from Jerry's only invitation; many friends in the UK, including Bill Wyman's wife Suzanne Accosta, to whom she is close, have also asked her to spend the festive season with them.

Extraordinarily, another close pal is Bianca Jagger — the only woman to whom Mick has been legally married — who lives in London. The pair have previously rung in the New Year together. Indeed, Jerry even invited Bianca along to her wedding to Murdoch.

Ever the diplomat — and all too aware that a little sugar can be a powerful tool in keeping potential foes onside — Jerry has recently intensified efforts to make alliances with the other women in Mick's life. Indeed, I can reveal that she has taken Mick's current girlfriend, American dancer Melanie Hamrick, firmly under her wing.

Melanie began a relationship with the Rolling Stone in 2014, not long after the shocking death by suicide of his previous girlfriend L'Wren Scott. Today, the pair have a six-year-old son, Deveraux.

Once a member of the New York Ballet, Melanie, 36, has embarked on a new career as a writer of Mills & Boon bonkbusters.

Described as sweet-natured and undemanding, she has been showing off an engagement ring since the spring of this year. I revealed that Mick has no intention of marrying again, and the ring is a mere symbol of her 'status'.

It's a potential romantic minefield, clearly. But luckily, Melanie has Jerry to guide her.

A friend said: 'Melanie will turn to Jerry for advice about her relationship. Jerry was one of the first people she told when Mick and she got 'engaged'.'

No doubt Jerry has advised Melanie on her 'engagement' with memories of her own Balinese wedding ceremony to Mick in 1990. She thought it was desperately romantic — but it turned out to be a dodge from commitment-phobe Mick, and wasn't legally binding.

When told she could have only an annulment, rather than a divorce, she said with admirable understatement: 'I didn't like the idea of annulling after 23 years and four children. It seemed a bit rude.'

As Jerry later reflected, Mick was a great dad but a lousy husband.

A friend says: 'No one knows Mick like Jerry. And no one knows how to be with him as successfully as she does. She wrote the book on how to deal with the infidelity, and how much space to give him.'

It seems that Jerry does not — yet — have a new man. Instead, there is a beloved new springer spaniel puppy, Spot, and she is concentrating on her children and grandchildren. Elder son James has a baby with wife Anoushka — the child pictured with his grandparents last week — although it's said they split some time ago and have now divorced.

Daughter Lizzie has son Eugene, three, with U.S. documentary producer Christopher Behlau. And, of course, Mick's daughter Jade has grown-up daughters, Amba and Assisi, who made him a great-grandfather some time ago.

A friend says: 'Mick and Jerry had their problems when they split up, especially over the house. But the fact is that they are each other's longest relationship and their grandchildren are a big tie.'

And now that any past tensions over money have finally melted away, that adds to the new-found harmony between them. Mick likes his women to be independent, and that, Jerry now certainly is.

The friend adds: 'In all honesty, Jerry was not that enthusiastic about working during the Jagger years. She would do a job if the money was ridiculously good.

'She would earn between half a million and a million a year — and then very comfortably manage to spend it all.

'Now, I'm sure she is really happy that she doesn't have to work any more. She loves spending money, she loves all the good things in life, and she loves rich people. And now she is one herself at last.'