Hi,
Rent a room relief is a flat £3750 for jointly owned property regardless of the split.
However you can choose not to claim this relief instead claiming under method A which is a simple profit less expenses.
You mention that your friend receives the rental 100%.
If you want to use this method you will need to declare the beneficial split to HMRC.
You should complete a form 17 as the property is jointly owned and attach a declaration of trust.
You can appoint a solicitor for this legal document:
TSEM9860
Thankyou.