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It is correct that his Transitional Protection has reduced by the amount he is now paid in rent.

I'd suggest looking at two of his payment statements, one before he moved and one after, to see if you can figure out what has happened.

You can also speak to a trained benefits advisor locally

https://advicefinder.turn2us.org.uk/

I suspect two things have happened, claiming Housing Element has wiped out his Transitional Protection, so that money he was getting in TP effectively goes to the landlord now, and there is a deduction for bedroom tax.

Could he look at getting a lodger?

https://www.citizensadvice.org.uk/housing/lodging-and-subletting/lodging-subletting/landlords-of-lodgers/taking-in-a-lodger-what-you-need-to-think-about-first

Lodger income doesn't impact a UC award, as per the information in the link.

Rent for supported or sheltered living is paid for by Housing Benefit (local authority).

As you mentioned his Transitional Protection reduced then I'm guessing it isn't classed as above so is paid for by Housing Element (UC).

I live in an adapted flat myself which is paid for by UC Housing Element.