The phone book entries are stored in the database. So here is a trick to pull them out.
Backup 3cx using the 3cx backup utility.
Open the zip file and you will find a file that is something like 1288930312Db.xml
Open the ???Db.xml with notepad
do a edit search for <Number>persons extension number</Number>
it should bring you to that person's extension
then scroll down and look for <PhoneBookEntries>
the <PhoneBookEntries> entry section should contain all of the personal phone book entries for that extension.
Cut and paste the section to a new empty notepad.
ie
<PhoneBookEntries>
<PhoneBookEntry>
<PhoneNumber>2045551212</PhoneNumber>
<LastName>Dell Repair</LastName>
<FirstName>Mark</FirstName>
</PhoneBookEntry>
</PhoneBookEntries>
now on the server b that the person has been moved to create a new phone book entry in the myphone app if it is blank.
backup server b.
follow the steps above to find the extension and the <PhoneBookEntries>, verify that it has the entry that you created above.
Cut and paste the PhoneBookEntries from the notepad file.
Save the ?????DB.xml file back to the zip file.
Restore the database.
Personally, I would do screen shots of the myphone phonebook on the old server and have the user retype them in on the new server. would be easier.
Also, if you have done any customizations to templates and other fun stuff, the backup/restore doesn't restore that stuff and it has to be added manually.
Jasit