We are not able to do much to help you as we don't have access to your database, nor to the procedure named "usp_WordMerge_SelAddlinesByFileNumber" which I assume is in the database.
I've used a SQL string to create the filtered recordset and then traversed that subset of data with the processing. This page shows the basic method
Using Excel VBA to Query a SQL Server Database | PTR
You will need to know the table (or query) name where the CustomerID field exists
Dim lngID as Long
lngID = 0947000 'assuming it is stored as a number
Set rs = conn.Execute("SELECT * FROM TableName WHERE CustomerID = " & lngID)
If your recordset is already filtered to a unique CustomerID then there won't be a need to test the values of that field since you already know what it is.