If your divorce judgment requires that you pay for the time share in alternating years, you can petition the divorce court to enforce the judgment and seek reimbursement of your payment for his share of the costs. Depending upon how long ago the judgment was entered and how long you have been paying the full cost of the time share, you may have issues enforcing the judgment or collecting the full amount you have paid on his behalf.

What is it that you hope to accomplish? For example, if you want to acquire the timeshare from your ex-, have you asked your ex- if he'll transfer it to you in exchange for your history of payment or for a mutually agreeable amount of money? If you want to sell the timeshare, have you asked your ex- if he wants to buy it from you (or accept transfer from you) or if he will agree to your investigating your options to sell?