It is possible, first you need to install Lightroom on the Desktop
Copy Or Move all the Images from Laptop and Lightroom catalog file
Once done Open the Lightroom on the Desktop and relocate the Images in Lightroom catalog.
Hope it helps.
The expiration of the trial does not affect your work that you did using the trial. If you purchase the software, all of your photos and all of your work will be available to you.
You would have to move everything to the desktop, as described in the link given above.