Pono Music World (PMW) is a variant of JRiver MC. As such, you should be able to do what's called a Library Backup in PMW. This will allow you to transfer all of your albums, etc, just as they appear in PMW, over to JRiver MC.
This may or may not be the easy way to do this. I started to type up a big description of this, but I'm not going to for now. Mainly because you're moving across computers and it could get kind of complicated.
Instead, maybe we need to figure out what's up with the files that don't show as albums. I'm guessing that these albums, like the Adel album, don't have any metadata. Like Album and Artist names for example. If you pull up those albums and look in the columns for Album and Artist, do you see anything there? I'm guessing they are blank.
If so, the only good way to make MC display them as albums is to fill in the Album, Artist, etc tags. You might be able to do this in a semi-automatic way, using the Fill Properties From Filename tool. The key here is to understand what data you are working with and why it shows up the way it does. Did PMW show all of your albums, including Adel 21, properly as albums?
Brian.