"If they can’t get a copy of the will does it go to probate?"
Just to add to what the pp said, it should be the original signed will but, if that has gone missing and you can find a copy of it then that can still be used.
If you can't find any copy of the will at all then his mother died intestate and the intestacy rules kick in. The closest living relatives then become the administrators of the estate.
What happens here is that either your partner or his sister (or both of them) apply to be administrators of his mum's estate. This is the same as being the executor of a will.
There's a guide here that explains what to do:
https://www.gov.uk/applying-for-probate/if-theres-not-a-will
Since there is a house involved then he and/or his sister will definitely have to go through the probate process and work out if there is any inheritance tax payable (it's unlikely that there will be any inheritance tax).
From there, the intestacy rules say that her estate must be divided equally between her children (or their descendants if one of the children has already died).
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"The property will need to be sold. Will it be a long process?"
We went through the probate process around four years ago so I don't know what it's like at the moment. I have read people here saying that it can be from a few weeks to a few months to get probate. After that, it seems that some homes are selling quickly and some are not if you have a look on the Property board.
"The daughter wants equity release now."
Well, that isn't going to happen, if you mean by that that she wants to get a mortgage from one of those equity release companies.
However, she will be entitled to half of the value of the estate and, if most of value of the estate is tied up in the house, then she will be entitled to that.
In that situation, the house will need to be sold or your partner will need to take out a mortgage to cover his sister's half of the house and pay her that. In that way, he stays in the house and the sister gets her share of the estate.