I'm a bit confused by your post, but there seems to be some confusion about overpayments in any case.
There are two separate issues. HB being recovered from the person to whom it was paid and, separately, any other internal admin / accounting between you as the payee and another organisation.
Where HB has been overpaid to the L/L, the LA can generally choose whether to recover from either the L/L or the claimant (there is an exception rule to this, but I'm trying to keep this simple(ish)). LAs are not supposed to have blanket policies (in fact, that is illegal), but most LAs will look to recover from the person to whom HB was overpaid.
The person from whom recovery is being sought most certainly has a right of appeal against being the target for recovery. However, the appeal right (re being the target) is strictly limited to "Judicial Review" grounds. In simple terms, the target will have to show that the decision to recover from them was wrong in law / completely unreasonable etc. However, there is nothing to stop you, as a target, also appealing against the calculation of the overpayment - the LA will have to show its overpayment is correct.
Once an LA has decided to pursue recovery from you and that goes ahead (assuming no appeal, or appeal unsuccessful etc), the arrangements you have with another party are entirely separate. Unfortunately, I just don't know enough about Housing law to offer any seriously useful comment - but I suspect much will depend on which party the tenant is legally liable to.
Hope the above at least helps as a starting point.
Regards
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