Transferring property following death

My mother died in July tis year and I am the executor/next of kin.  Probate was recently granted in my name.
My father died last February but I don't think their property (which was owned - no mortgage) was ever transferred into my mother's sole name, unless this was part of the Tell Us Once service undertaken when reporting his death.
So I have two questions - how do I check if the property is in my mother's sole name and as I will be soon moving into the property, how do I go about transferring it into my name?
 

Hi Jon

I am sorry to read of your loss. 

Our online assisted guidance explains how to transfer the ownership when buying out the other beneficiary. Complete the Qs asked and the correct guidance will then be revealed with links to the required forms etc
If you have not checked the current registered information for the property then we would always recommend you do so before applying to update it

You will need to contact HMRC to query what stamp duty issues/payments arise