Exchange will find the public folders no matter what server they are on when using the outlook client. To replicate current folders over to the new server you have to manually add the replicas. They do not replicate automatically.
You have not said what version you are using of exchange, so how you replicate depends on that.
You can use Exchange System Manager in ex2003 to add replicas folder by folder, or you can download PFDAVAdmin tool 2.8 from microsoft and do a bulk operation to add the replicas to all folders at once. This is by far the easist way and will work with exchange 2007 as well. You install the tool on your pc, not the exchange server. It requires .net framework 1.1