I have a Samsung Galaxy Note 2 from T-Mobile and I'd like to know if a Sim from a Verizon Galaxy Note 2 will work in it.
No, T-Mobile is a GSM network and Verizon is CDMA, so their devices are incompatible across networks.
demmo is wrong. This is a world phone. Supports both GSM and CDMA. Problem would be getting Verizon to enter your EMEI into their super duper ultra top secret locked database to allow activation.
And with all that ... the answer is still "No".