Thank you. You are right to express concern.
However, there is no reason why the solicitor that is arranging the transfer into your mother’s sole name cannot advise you in respect of this.
What you need to do is get your mother to exercise a deed of trust whereby although the property is in her sole name legally, the equitable estate (financial) of your father share still vests in the children.
To satisfy the revenue that this was not a sham created at some later stage to avoid paying inheritance tax on the whole price, it would be advisable to have the trust registered against the property as a restriction. That way, can prove that the trust existed at the time of the transfer and that it was only done for mortgage purposes.
Can I clarify anything for you? Please rate the service positive so that I get paid. We can still exchange emails. Best wishes. FES.