Making A Mountain

............... we’ve got a very naughty mole who is gradually digging further and further into the lawn :-(
We’ve lived with/tolerated a mole in the garden for many years now because it mostly dug it’s tunnels around the back border and didn’t seem to be too destructive. We think that last year the current occupant of the tunnels ( apparently they don’t live very long but a new occupant very often moves into the existing tunnels) strayed under the fence into next door’s garden because they suddenly acquired a very annoying ‘ mole deterrent’ that buzzes every 40 seconds or so ( they are supposed to be inaudible to humans but we could hear it very clearly!!!).
It obviously didn’t work because my neighbour asked me for the name of the pest control company that we used for the rat problem .......... a while after that, the new molehills stopped appearing in our garden.
A few months ago, they started again with a vengeance - this time all over the lawn - it looks a right mess now.
I’m in a quandary because I really don’t want to have someone ‘deal’ with the mole ( another one will only move in anyway) but it’s destroying the lawn.
I just wondered if anyone out there has successfully lived with a mole in residence and if so, if they have any tips on garden design to take account of the constant digging. HELP :-/