Can I turn a Straight Talk phone (Galaxy SIII) into a T-Mobile carried device?

[Rubyknight294]

I recently purchased a Galaxy S III for Straight Talk, and so far the service hasn't been pleasant. I talked to a representative from Straight Talk and they blame the poor service on maintenance on nearby towers (Which I guess it uses SPRINT towers), but what happens is I get 0 service in my house, and when I leave, it's instant 3G with 3-4 bars. So I'm in a slump, and am interested in switching to T-Mobile, which has nation-wide 4G coverage.

So can I convert my ST Galaxy SIII into a T-Mobile carried device? If so, how? I know it has to do with a sim card, but as this is my first smart phone, I know very little. Thanks if you can help!