You could try creating linked servers using the special stored procedure, sp_addlinkedserver (you can read more about this in BOL for full syntax and options).
To relate this to your question let us assume that both your databases, A_DB and B_DB are held in 'ServerOne' then A_DB is moved to ServeTwo. The sproc does not know that A_DB is no longer in the same server so it will not work.
First we create a linked server, something like this :
exec sp_addlinkedserver @Server = 'ServerTwo',
srvproduct = 'SQLTeam OLEDB Provider'
Check to see that your linked server has been added by using sp_linkedservers, like :
All you need to do now is modify the code in your stored procedure so where there is a mention of any object in A_DB you will need to do something like this :
select * from ServerTwo.A_DB.dbo.someObject
Hope this helps.
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