You should convert to phpbB3. phpBB2 is nearing the end of its support life.
The convertor that comes with phpBB3 should convert most of your information. To keep the BBCodes of phpBB2 Plus on phpBB3, you will want to add the BBCodes that do not come with phpBB3 to phpBB3 prior to conversion. See Custom BBCodes
After the conversion, you will probably have to move some of your forums will make your subforums into regular forums. You will also need to check your permissions.