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Thank you for your question
My name is Clare
I shall do my best to help you but I need some further information first
have you already appointed a solicitor to deal with the sale?
There are two options.
The simplest is to simply give written instructions to the conveyancer (expressed as being irrevocable) to pay 50% of the equity to this other person.
The Conveyancer can then confirm that they have those instructions to that person at the start of the sale process.
The other is a Declaration of Trust - which need not take time but is superfluous if a sale is imminent
I hope that this is of assistance - please ask if you need further details