I think the best thing you can do to ensure that your son's rent account is up to date is to contact your landlord . Housing Benefit should credit the rent account up to Migration and you also get a lump sum of 2 weeks Housing Benefit Run On. After Migration the rent should be covered by UC Housing Costs. You also stated that your son may not move at all and the landlord may not be happy to answer hypothetical questions.
David
Nothing on this board constitutes legal advice - always consult a professional about specific problems
I shall ensure the rent account is up to date when/if this happens, that's an idea I hadn't thought about, thank you David. The landlord is always very helpful - it's a small housing association which lets flat to vulnerable people.