Yes, +1 to dafloyd.
JRiver uses Vorbis Comment as a base (not sure what Media Monkey uses btw, but ratings are often handled differently between programs even if it uses Vorbis which it might)
You can use grouping as well as a number of other fields temporarily. Here's a slightly outdated mappaing list
http://wiki.hydrogenaud.io/index.php?title=Tag_Mapping. Grouping is a good choice if you are not using it already.
First though understand that currently JRiver support 5 stars (numbers 1 through 5, with no half stars) So if you have ratings of 4.5, or 9 you will have issues -- they can be fixed later, but won't work on first import, you'd have to convert the scaling. Make sure that MM is writing the tag to the file. I think it does this but its been a long time since I've used MM.
After you have copied over the ratings to a field like grouping, either you would want to remove the tracks already in your library (MAKE A MANUAL BACKUP of the JRiver Library first File=>Library=>Backup takes seconds btw). And then redo an autoimport. Probably the easiest if you have not started retagging in JRiver yet. OR Select the files in JRiver and right click choosing Library tools=>
Update Library form Tags If something screws up simply click CTRL+Z or restore the library backup you just made.
Now you can make a bul change by selecting the files you could select them for ALL the files at once or try a couple of albums first and then select the rest (reminder you do have that backup handy right?
)
Open the tag window and make sure you see the grouping field (click on the icon top left corner and you can also show the grouping field and the rating field if need be).
Then simply type this in the
[RATING] tag field=[Grouping]
if you have chosen not to use grouping you can just put the name of the field between brackets =[FieldName].
If this works for you, make a second backup of your library giving it a new name. In case you find you made an error you can go back and forth using the two backups.
I'd recommend clearing the Grouping or temporary field later, as you might find some use for it.
Post back if you have problems.