Question

It’s a MS Access app with linked tables to SQL Server. I need to log this on the SQL Server as I cannot modify the MS Access app.

The app connects to the SQL Server through a default SQL username.

Answer 1

You will need a trigger for this, and a table to store the results. Very quick prototype:

CREATE TRIGGER dbo.trigger_name
ON dbo.table_name
FOR DELETE
AS
    INSERT INTO dbo.LogTable(RowID, UserName)
        SELECT PK_Column, SUSER_SNAME()
        FROM deleted;
GO

Note that unless each Access user authenticates to SQL Server as themselves, you may need to use host name or some other property to identify them (if they all connect as the same SQL user, there is little SQL Server can do to determine who they really are).