Depends. Did you save the installer package, or install it directly while downloading? Basically, you can't copy an installed program between computers.
Why don't you spring for a new piece of photo hardware. Most of them come with free copies of Adobe Photoshop Elements or similar.
All that said, most of today's software requires activation, rather than installing a serial number. Hence, you can only install it to the limits of its EULA. Adobe allows 2 installations of its photo software product. (And hence 2 activations of the same license). The express intent of this relates directly to your situation, one for the desktop, the second to your laptop.
If you have serial number activated product, then obviously the number of installs are between you and your conscience. Please don't share this with us.