By default, once minimized an RDP session stops displaying the screen.
As a result, when the Remote Support client is started in an RDP session, minimizing it will prevent anyone from controlling the screen until it is maximized again.
To allow screen control even if the RDP session is minimized you will need to follow theses steps:
Step 1: Close the Remote Support Client on the RDP session you are in as well as the RDP session itself.
Step 2: On your workstation, download and run this reg file available here.
It will create the DWORD registry key RemoteDesktop_SuppressWhenMinimized in HKEY_CURRENT_USER\Software\Microsoft\Terminal Server Client and assign the value 2.
Step 3: On your workstation, open a new RDP session in which you want to share the screen, then start the Remote Support Client inside the RDP session.
You will now be able to minimize the shared RDP session without interfering with the person currently controlling the screen of the RDP session.