Your Masonic membership is normally "transferrable", provided that the Grand Lodges of the lodge you are leaving, and the Grand Lodge of the lodge you choose to join are in communications. If you move within a jurisdiction, like from Texarkana to El Paso, you can transfer your membership. If you transfer out of state, the Grand Lodges must be in communications. Some Grand Lodges permit Masons to hold multiple memberships, both in-state, and out of state. I belong to lodges in Kentucky and Massachusetts. Best way, is to check with your lodge secretary, and contact the Grand Secretary of the Grand Lodge in the state you are transferring to.
I once moved to Ohio. At that time, Ohio permitted Masons to hold only one (1) lodge membership at a time. If you wanted to take out a membership in an Ohio lodge, and you were moving in from another state, your application had to be accompanied by a demit, from all of the lodges you belonged to, before your application could be accepted.
The Grand Lodge office is the best source of information in your state(s).