Adjusting Tax History Summary P070920, will it adjust Historical Register and W2?

I need to adjust the Gross Wages and Excludable Wages for a Federal A tax because the system didn't write it correctly into F06136 during a payroll processing period. If I go into Tax History P070920 and update the Gross Wages and Excludable Wages for Federal A should I see that adjustment reflected in the Historical Register? I tried it and did not see my Historical Register change. Is there somewhere else I need update the Gross Wages and Excludable for Federal A? I also need this update to flow into the W2.