The groups on Lismore, Mull with Iona and Kerrera are among 141 groups in all across Scotland getting a split of £7.3 National Lottery funding.
Officers called at a property on the island on Saturday, one day after Marks & Spencer chairman and former Tory MP Archie Norman dismissed rumours that he and his family had arrived on Lismore after lockdown.
Former Tory MP Archie Norman confirmed his 35-year-old daughter is on the island independently.
They had hoped to lay a relative to rest next to his family on the island last week, but had no idea the cemetery was at capacity
The identity of the new proprietors, who will also run the Post Office counter, is staying under-wraps for now but they will take over in August.