Is this somehow possible?!?

I've never heard of them transferring someone else's debt to another account (X's debt to Y's account). Since it's a local company maybe they will do it. If your sister did agree I'm not sure why she would be mad unless you did actually do it without permission. I'm not understanding why someone would be mad when she agreed to it and you're paying on time (?). The best thing would be to open your own account next time. Pay that account off in full forget about waiting if she's all mad about it. You could see if they will allow you to transfer it to an account under your name (no guarantee).