Yes, there is a document for moving BSE from one server to another. Just go to InforXtreme and search for the same in Documentation as I am not sure about the document code.
Also, some basic things to check are- (if its Windows)
1. Check the permissions for $BSE, $BSE\bin, $BSE\tmp folders.
2. Check if everything is fine in $BSE\lib\ipc_info file
3. Basically, there are a set of files you need to back up from old BSE to new BSE before overwriting which you will find in that document.
I am assuming both the Servers have identical environment, similar installation directories, new environment has proper SLM installed, Same types of databases, same users. Also, make sure you backup and restore the databases too in order to sync the systems.
If you don't have to sync the databases, you will need to backup some files like tabledef6.2 etc.
I will suggest you to go with the standard document. Its easy if you go following all the necessary steps.
Here are some threads-