Will a Tmobile samsung S4 work on verzion network
Will a T mobile Samsung S4 work on Verizon network
No... it lacks the CDMA and full set of LTE radio bands to function on Verizon's network.
No, T-mobile and Verizon's networks use different signal bands.
Regardless of radio bands, one is CDMA and the other is GSM. Just not possible sorry.
To change network in Samsung S4 it needs to be unlocked. Once unlocked it can accept other GSM networks but not CDMA networks like Verizon. To unlock, I suggest you can approach Simpleunlocking.com and specify the country,locked network of Samsung S4.Based on the availability you can get the permanent unlock service along with free instructions.