No, she is keeping on the mortgage it would need to be agreed by the lender (make sure she can afford it on her own etc...) and, if they agreed, a formal transfer would need to be done (along with any formalities for the lender) and it registered at the Land Registry.
If she is not keeping the morgage eg getting her own by remortgaging to get the funds to pay him off, a formal transfer would still need to be done and registered at the Land Registry, also taking the old mortgage off and putting any new one on.