For U.S. tax purposes, foreign depreciation does not figure into this at all. Your cost basis is the *lesser* of what the giver originally paid for the property plus any property improvements, or the FMV at the time *you* placed the property in service. I doubt the property is worth less than the giver originally paid for it. So I would expect your cost basis to be the giver's cost basis.
Foreign rental property placed in service in 2018 or after is depreciated over 30 years. The TTX program can handle that just fine.
