Hey @JefferyAndre,
That's actually a great question! Since we don't have a comprehensive "How to" guide for this, how do any of us know what's
normal and what's not?
Regardless, your suspicion is correct: The messaging should be fully linked, bi-directionally -- a message sent from the phone will appear in the Win10 app, and a message sent from the Win10 app will appear on the phone.
Of course, the operative phrase is "should be", right?
Dave
***NOTE:***For anyone interested, I read a pretty good article about the Your Phone Companion app in PC World's Feb 25, 2020 issue, title "How to use Windows' Your Phone app to connect your phone to your PC" by Mark Hachman -- I'll
let you find it, if you want to read it. It nicely describes what should be happening, and also describes certain features we'll (hopefully) see in future versions of the App and OS.