When Remote Desktop has two screens to use remotely

onfiguring a multiple-monitors connection

Launch Remote Desktop Connection in the normal way.. .Expand the Remote Desktop Connection window so that you can see all the tabs. Choose the Display tab and select the Use All My Monitors for the Remote Session check box, as shown. Then return to the General tab and click the Save button.

When you connect the remote system's monitor will be reflected in your multiple monitors,the sameas if you were physically at the remote system.