Export Firefox bookmarks to an HTML file to back up or transfer bookmarks in Firefox 7.0.1 on your laptop, putting the bookmarks.html file on a memory stick and then Importing bookmarks from an HTML file in Firefox 3.6.20 on your desktop should work.

Here's another way:

Restore bookmarks from backup or move them to another computer

In Firefox 7 on your laptop, save a bookmarks backup file, which will be named "bookmarks-<today's date>.json" (e.g. bookmarks-2011-10-14.json) then save it on a memory stick. In Firefox 3.6 on the desktop computer, use the Restore feature and the "Choose File" option and select the backup you placed on the memory stick.

If you have problems with the memory stick, you can also try e-mailing the bookmarks backup file to yourself, save it to your desktop or other location and then restore it.

I tried the bookmarks.html method. Didn't work.

how do I save the .json bookmarks backup file? There is no such command in my bookmarks bar.

Never mind, folks. I figured it out. Thanks for your help, Alice.

You're welcome. So, what solved it?

I was going into the Show All Bookmarks window, then selecting Export Bookmarks From HTML, which was saving a Safari version of my bookmarks (I'm on Macs). Once I selected backup instead, it gave me the .json file I needed. Put it on a memory stick, imported it on my desktop, and I was good to go.

Thanks for your efforts. Without the tip about the .json file I probably wouldn't have figured it out.