Can he afford to get someone in to do the work? Are the shrubs growing in his garden?
If they are in his garden then there surely would be no problem with the lease if they are pruned properly. I don't know what the legal position would be if he wanted to have them removed.
Even if not I guess he would be within his rights to have someone come and prune them so that they don't damage his property.
But it would be polite to mention the problem to his neighbours if they are their shrubs (whether related or not). Say that he will get someone to do the work unless they would prefer to do it some other way.
Maybe this does belong in the legal section. All I know is that you can remove your neighbours branches if they overhang your property, but you have to give back any timber or fruit. (least that's what the books said 50 yrs ago)