Swiss International Airlines - Mileage run FRA-BUD-TXL - check luggage

Hi,

I am doing a little run from FRA to TXL via ZRH and BUD in order to rack up the missing miles for SEN requalification this year.

I have 2 bags that I need to take to Berlin.

Is it possible to check them through from FRA all the way to TXL? Or would I need to recheck them in BUD (which is impossible given the 40min turnaround)?

Thanks for your help :)