Supporting a parent getting Housing Benefit without affecting entitlement?

Wondering if anyone could provide some guidance:

We have a parent receiving Housing Benefit. Only other income is Pension.

We want to understand whether there's any impact on entitlement to Housing Benefit if some financial support is provided - we think something in region of £600pcm - which would be £7,2k p/a. Would that impact entitlement to HB?

Context: HB is max for LHA for a one bedroom flat. Part of the £600 would cover the gap between the LHA and the actual rent on a potential new place, where they want to move to.

Thanks!