ESA payments suspended two years ago, due to gift - what now?

My family member was on ESA, and was gifted a fair bit of money around two years ago, which pushed their savings above the £16,000 threshold, so their claim remained open (so NIC were being paid etc.) but they no longer received actual ESA payments.

Now, however, their bank balance has dropped to below £6,000 (the lower threshold), so we are thinking of reinstating the claim. At the time the payments were stopped, we were told that we would probably have to apply for UC when the claim was reinstated. Next week, I will call the DWP and ask what happens next, but I also wondered if there was any pointers, roadmap or advice that the forum mods could let me have...will we have to apply for UC? Will this involve being reassessed as if for ESA? The claimant's medical condition has remained completely unchanged for the duration of this recent unpaid episode; the condition is untreaable so we don't have any 'new' medical notes to support such an application, although we do have the original communications from the GP, of course, from years ago.

Any advice, please?