Hi, welcome to phpBB.com!
I'm not sure what you mean with moving all accounts. There's not really a way to merge a MyBB board into an existing phpBB board and keep all the data that was already on the phpBB account as well.
What is possible, is to convert your MyBB instance to a phpBB board. You'll need to do that in two steps. First you can use this convertor
to go from MyBB 1.8 to phpBB 3.1. Then the last step is upgrading phpBB from 3.1 to 3.2, which should be fairly straightforward, and the instructions for it are over here