put your axolotl in a tub be prepared for it to be in there a couple of days, if you have any ornaments/caves etc.. put them in a bucket/container with old tank water, put the filter if it is an internal into a container with old tank water, empty the tank and move it.
refill tank half way with dechlorinated water running a air-stone in the water then leave it over night, following day put any ornaments/caves back in tank along with old tank water, place filter back in tank. start filter up. wait couple of hours and check parameters are correct, if trace's of ammonia found retest after 24hrs, it is normal for ammonia to be found after a water change because dechlorinaters remove the chlorine from chloramine leaving ammonia. if all is good put axolotl back in the tank.
whilst the axolotl is tubbed make sure to change water every 24hrs.
if the tank requires topping up do so after 2 days so it has had time to settle, might be a idea to get some bottled bacteria in case the bacteria colony has been harmed.
test the water regularly to make sure the cycle hasn't been damaged in the move.