In the transfer deed you will state that the consideration for the property is what the mortgage co have stated but that it comprises x% as cash and y% as a gift (i.e. if the mortgage co state the pp as 100,000 then the cash element would 80,000 anf the gift element would be 20,000) – you will only pay stamp duty on the cash element.
Your fil will need to complete a declaration of solvency as the transaction is at undervalue (and as such could be set aside) and you will need to obtain a policy of defective title insurance to cover fil’s possible insolvency – your mortgage co will want this – premium depends on amount of loan = could be a couple of 100.
If the property was not and has never been fil’s principle private residence the there will be a potential charge to cgt – fil could transfer a half share to mil to claim two cgt allowances (11,000 each), assuming there is a mil to help offset any gain – cgt would be payable on the total of the cash and gift elements. If the house has been in the past fil’s ppr then he may still claim some ppr relief and likewise if the house was subsequently let – you would also knock off the last 18 months of ownership
fil’s estate may be subject to iht on the gift element only if he doesn’t survive the 7 year (known as a failed potentially exempt transfer)and this would be in addition to any cgt paid so an element of double taxation.
This is a very common scenario so not sure why your conveyancer is getting upset.