I assume the Scrapbook extension is installed on the new Firefox.

It may be that Scrapbook is not aware of the individual added folders. If there is no command to re-scan and re-index them, you may need to copy the entire old Scrapbook folder to your new Firefox in order to have everything recognized.

Thanks jscher - but my Firefox profile is in my data partition. I wish to copy my short-term Scrapbook items to my User App data in the OS partition. So all I want to do is to copy the Scrapbook folders into the OS partition of the other computer and have them recognised by Scrapbook. The reason for this is that I keep my long-term scrapbook folders (that I keep for reference) in my data partition, where they are automatically backed up. The folders I want to transfer to the OS partition of the new computer are short-term items (eg, magazine pages) that I do not want in my data partition (as backup is not needed).

Sorry, I don't use Scrapbook myself so I have no direct experience with that extension. There is a Scrapbook support page here - http://www.xuldev.org/scrapbook/
Have you read the Tutorial PDF (available on that page) to see if there is any mention of merging data from different Profiles or other devices? Keeping in mind that Tutorial is for a much older version of that extension - V 1.2.

Have you looked for an add-on for the Scrapbbook add-on to merge Scrapbook data from two separate installations?

http://www.xuldev.org/scrapbook/misc.php

Where are my collected data stored?

They are stored in 'ScrapBook' directory in your profile folder. The file named 'scrapbook.rdf' is a XML/RDF that manages tree structure of your collection, and each items you collected are in 'data' directory. 

My guess is that you need to edit the scrapbook.rdf file to recognize additions to the 'data' directory, by merging the two different rdf files and then stripping out the duplicate code for the start and end of the rdf file which would appear in the middle of the "merged file". One complicating factor is the complexity of the folder setup in both of the original files, and how you copied the individual "scraps" into the 'data directory'.

If you have ever done any HTML or XML coding "by hand" in a text-based program, you might be able to handle merging the scrapbook.rdf file. Otherwise your chance of success is limited.

Many thanks Edmeister - looks complicated. Also for some reason the links in your reply did not link.

I think the easiest way is to copy the Scrapbook folders onto a stick and place them in a folder on the second computer (or zip them and email them). The full pages can then be accessed by double clicking the Index.html files (after unzipping if necessary). This is a bit cumbersome, as you have to run Index in each folder (ie, there is no way to automate it as in Scrapbook proper). However, since Windows Explorer remembers your searches, it is quite quick and effective. I think that is easier than playing around with the rdf files.

Please if possible send the link to the pdf file that you mention.

Did you try those links from the email that was sent to you, or from this forum page? Those links work here in the forum.

If you are unable to open the http://www.xuldev.org/scrapbook/ website, this link to the PDF Tutorial probably won't work either.
http://www.xuldev.org/scrapbook/files/ScrapbookTutorial-1.2.pdf