It should work but I doubt 3G or LTE will work with T-Mo. T-Mo uses different 3G and LTE frequencies than ATT.

 

I was unaware they have added 1900mhz support on their network. If their network frequencies match the supported rugby pro frequencies you should be ok i'd think. You'll need a sim unlock though to move it over.

Check out gsm arena or phone arena for the specs on the rugby pro radio, if things match up you should be ok.