Yes... correct...
Whatever facilities were built before(except fort lvl), once it was being destroyed, the new land owner who setup new stronghold will have all the previous facilities...
point to take note:
1) upon destroyed, if you rush to setup new stronghold, the fort level will be just lv-1 with 10 durability ONLY.
2) if you find the location is strategic enough, simply capture all surrounding enemy lands before setting up the stronghold.
3) failing above, you will simply ended up enemy repossess the stronghold will all his previous facilities and his protected lands..