If your wrote that simple select is not working, the issue is in security configuration of the linked server and permissions which your user receive there.
Among this, when you execution your query, you don't need to specify the server name and DB name for both parts - source and target. You simply need to execute the query on target server and target database. In this case your query instead of
INSERT INTO [Target_server].[Target_DB1].[dbo].[Target_Table1](Target_Column1)
SELECT Source_Column222
FROM [Source_server].[Source_DB1].[dbo].[Source_Table1]
WHERE Source_Column1 = 'ID7162'
will looks like the following:
INSERT INTO [dbo].[Target_Table1](Target_Column1)
SELECT Source_Column222
FROM [Source_server].[Source_DB1].[dbo].[Source_Table1]
WHERE Source_Column1 = 'ID7162'
and you need your connection to be opened on server [Target_server]
and database [Target_DB1]
. Also the linked server security properties need to be checked on [Target_server]
against the [Source_server]
.