If the tenant is applying for housing benefit, what shall I do?

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Hi, I recently signed AST agreement with new tenants introduced by agency. They are a couple with a young child. Before entering into agreement, the agent told me they did all the checking against the lead tenant (the husband). After signing the agreement, I was told that they had divoced and the husband is actually not living at the property. The ex-wife is an Australian and looks much older than the ex-husband (who sounds very local to me). She said she just arrived in the UK and is planning to apply for housing benefit. The ex-husband asked me to send her a letter with the amount of rental and say yes to the local council when I'm contacted by them. Would that give me trouble in the future?

I have heard a lot of stories regarding dispute with tenants who are on housing benefits and I don't want to take the risk of making another one myself. The ex-husband promised that he will keep paying for their rental, but can I evict them after the initial term of 12 months given a proper section 21 notice is served?