How to save firefox addons for offline installation

On the Firefox addon page search for your desired addon.

Download Addon

1. Continue to download
2. Right-Click -> Save Link As... -> save the .xpi file

Installing Addon

Drop the addon in the adress bar.

Possible. If you need only the Add-ons to be saved & install offline, you may refer below steps. Or if you're planning to do a full backup, you can also refer Journeyman Geek's Answer.

1. These files are usually .xpi or .jar files.
2. Download the file to your local computer.

3. At the top of the Firefox window, click on the Firefox button, and then click Add-ons. The Add-ons Manager tab will open.
4. In the Add-ons Manager tab, select the Extensions panel.
5. To add the downloaded add-on to the list of available add-ons, drag and drop the file into the Add-ons window. The Add-on is added to the list.
6. The installation process should begin.

That should get your work done.

Source: Mozilla Support