Surrender of Tenancy by Tenant

Tenancy Types and Management

I have agreed with the tenant to them ending their fixed term tenancy early on the basis that they provide 3 months notice (they have 8 months left on their agreement), so that the tenancy will end after the 3 months. However, as the tenant is keen to end the agreement as soon as possible, we have agreed to end the agreement as soon as the property is relet if it is before the end of the 3 months (they have mostly moved out anyway).

I want to be able to confirm this agreement in writing to them, but all of the templates I find are for an immediate surrender deed and not after the expiry of a period of notice. Is there a way to do this? I know lots of advice in this situation is to let them leave when a new tenant is found how is that formalised? I want to given them the certainty that there will be no additional liability.