Yes, you can take the deduction. In general, the person paying the expense gets the deduction.
You can deduct interest on a timeshare if it is deeded and recorded in public records and it meets all the requirements for deducting mortgage interest.
Mortgage interest can only be claimed on a maximum of two homes (main home and a second home). If you have mortgages on two homes and a timeshare, you won’t be able to deduct the mortgage interest on one of those properties.
Click here for additional information on timeshares and mortgage deductions.