You can right-click the blue add to Firefox button on the Add-ons website and download (save) the extension (XPI) file. You can use a USB drive to transfer the file to the other device. You can drag the file to a Firefox window or use the cogwheel button on the about:addons page to install a locally saved extension.

• https://support.mozilla.org/en-US/kb/find-and-install-add-ons-add-features-to-firefox

I found it easier to do it the way cor-el describes by using a different browser. When you visit https://addons.mozilla.org/en-US/firefox/ and navigate to an add-on you will see a Download File link underneath the blue button (see image).