I don't know about other forum systems, but I'm sure miniBB can handle such kind of tasks in 99% of cases. I'm myself have implemented a lot of integrations for our customers, and they all work well. You just need to be sure your current users table has autoincremental integer ID field, which miniBB will be tied with. All other stuff can be additionally configured. Take a look at our synchronization guide
or Paid Support section
- we're providing such kind of custom implementations for the fee starting from just US $55.