My scenario: Computer A has an Access database that contains linked tables. Those linked tables actually reside in another Access database on Computer B. Nothing unusual y
Nope - you can only link to real tables - you have to recreate the SQL server links you did on database B for database A
If the SQL server data does not change much and you are just using it for lookups you could import the data into real Access tables which you could link to.
EDIT
Another solution is to link the tables dynamically - that way you don't have to add the DSN manually to each computer. Use a connection string something like this:
ODBC;Driver={SQL Server};Server=;Database=;UID=;PWD=
This links a table
Dim db As Database
Dim TD As TableDef
Dim sTableName As String ''MS Access name (can be same as SQL Server name)
Dim sServerTableName As String ''SQL Server Name
sTable = "Table1"
sServerTableName = "dbo.Table1"
sServerConnect = "ODBC;Driver={SQL Server};Server=Localhost;Database=DB1;"
Set TD = db.CreateTableDef(sTableName)
TD.Connect = sServerConnect
TD.SourceTableName = sServerTableName
db.TableDefs.Append TD
db.TableDefs.Refresh