Well Hugh, she needs not have contact with HMRC, she would almost certainly be deemed to be non resident and although she is required to declare any income which has not been taxed everybody appreciates that a mere couple of thousand is well below the personal allowance so a declaration is merely an exercise in financial and administrative futility!
Well, you could proceed as you suggest, but why throw away half the tax free rental under Rent a Room relief? It is always possible that, if you put a case to them, HMRC will allow full relief. They can only say no so write to your tax office explaining the situation in which you find yourself. Not all HMRC staff are ogres.
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