Solution to remember a window's size and position for laptop built-in monitor vs external monitor on Windows?

Actual Window Manager, among other things, allows you to restrict the size and position for your elements. Believe me, I tried to solve a very similar problem for years (remember window position and size accross three screens), and this is the closest I got to it. Besides, it's an awesome app, allows you to control multiple aspects of the windows GUI, and supports profiles, which would allow you to accomplish your goal.

Specifically, once you install the app, double click the tray icon, then under window settings, right click specific settings and select Add window rule. then on the right pane go to the target window tab and select the app you want to control. After that, you can control its position under position -> restrict placement, and its size unger Size -> fix minimal size and fix maximal size.

After you've finished configuring it, right click the tray icon and select desktop profiles -> configure.

You want to end up with one profile with position/size rules for fullHD and another for when your laptop is undocked.

I just tried a program called Mosaico that seems to do almost exactly what is wanted except that it can't handle full screen windows well on my computer.

Also, another downside is that it is not free, although there is a trial period.

http://www.soulidstudio.com/#mosaico_features

Edit:

I also use Display Fusion which has some of the options described in Actual Window Manager if you need an alternative to that option.