To remove the ex-partner from the mortgage your parent will need to carry out a 'transfer of equity'. That said, the ex-partner will have to agree to this as they will have to sign the legal documents too. So they may ask to be 'bought out'. It should also be considered that the lender may then assess your parent's ability to pay for the mortgage on their own, as when they applied for the mortgage there would have been two incomes used for assessment.
I would recommend that your parent seeks legal advice.