Regardless of the domino version that you are running you could start off by......
1. Installing the OS(and any OS configurations that's necessary) on the new hardware
2. Install domino (same version as on original BES server). Don't configure anything as yet.
3.Copy the following files from the Old BES2.2....You will have to shut the services (domino and BES) down, or else you'll get "sharing violation" errors when youo attempt to copy files.
a. Notes.ini (pay special attention to the path statement in this file.....should you change your install directory structure on the new hardware)
b. Server ID (should be named your "domino_servername.id"
c. Names.nsf (public address book replica)
d. BES folder...this is a sub-directory in the "Data" directory. This folder contains the all the BES specific dbs.
Once you have copied thes files and folders....you can startup the new domino server and check the console and logs for any errors. DO NOT START THIS SERVER ON THE LIVE NETWORK. DOING SO WILL CAUSE DISCONNECTION FROM THE NOC. Not to mention the a server with the same network name and domino name will cause severe internal network problems. So I'll assume that you 'll be doing this on an isloated network.
HINT: Doing a File Copy through the network is the SAME as creating a replica in Notes. Thus the dbs will all retain the same NoteID as the original dbs.
Once you have verified that there are no "disturbing" errors. Refer to the upgrade requirements as far as software is concerned, before proceeding with the 4.0 upgrade.
When that's done extract the license from the BESX version and insert into the new install via the BM tool.