Edit in PS from LR doesn't work after moving software to SSD

Moving applications is not the best way to free up drive space, your files (photos, music, video, etc) take up much more space and can be stored anywhere. Leave the apps where thay are installed and move the other stuff instead.

Moving the software applications to another drive is not a good idea. You will also get problems when updates are needed. The Creative Cloud app expects the apps to be in your Applications folder on your internal disk, if they are not, then it probably will install new copies in that place as soon as you try to update something. That means you will have two copies of your apps with different version numbers (the apps on the external drive probably won't be removed). The Lightroom and Photoshop applications are not so big that moving them to an external drive makes a lot of sense either. At best you win one or two GB disk space. If you want to regain disk space, then consider moving your catalog folder and your images.

When the 'link' between Lightroom Classic and Photoshop has issues, the first step is to try this:

Use the Adobe Creative Cloud Application to uninstall Photoshop. When asked, keep preferences! After this reinstall Photoshop again.

If this doesn't help the nest step is to reinstall both apps Lightroom and Photoshop. Please folloe the steps below:

1. Open the Adobe Creative Cloud Desktop Client and uninstall both Photoshop and Lightroom Classic. When asked, keep preferences! 

2. Install Photoshop first and then Lightroom Classic. The right order is very important here!

If this doesn't help try the reinstallation with removing the preferences also.