Is it possible to pass a stored value entered from one screen to another screen if they are both open at the same time?
You can pass a value to another (open) screen in exactly the same way (fpmi.openWindow) as you would open a closed screen with parameters. This function sets dynamic properties in the Root Container of the target window, plus gives it focus. The Window Navigation training video covers this.
Alternatively, you can reference a client SQLTag and write to/read from this between windows.
The rest is just binding to the SQLTag or Dynamic properties on the Root container, as the case may be.