Again, thanks for your replies and help. And again, I apologize for the questions which might be obvious to others - I'm only 1 week new to Joomla, and I've been searching and reading and learning as much as I can.

slabbi wrote: This is only cosmetic since you have not updated the language file.

I updated the english.php file you pointed me to above. Is that the language file you are talking about?

slabbi wrote: When you switch off SEF you will see that uddeIM creates the link correctly.

ahh, ok... I didn't realize that SEF was involved here (I'm sure that points out just how new I am to all of this). I turned off SEF in the Joomla global configurations, and now I'm looking at the URLs for everything, and learning just a little bit more.

slabbi wrote: To ensure that we are talking about the same: You have selected uddeIM and see the inbox. When you click on someone's name uddeIM should redirect to the corresponding Kunena profile.

This is correct.

slabbi wrote: uddeIM profile link as mentioned in the subject is a completely different program: It is a CB plugin that displays a link in a user's profile to the uddeIM compose new message page and has nothing to do with Kunena.

OK, that was a misunderstanding on my part, then. I do not have CB installed at this time.

slabbi wrote: Itemid 135 is the correct one for Kunena?

No, itemid=135 belongs to the uddeIM inbox. The Kunena profile is itemid=120.

slabbi wrote: Do you have a SEF component installed? If so can you switch off SEF for uddeIM?

No, I don't have any SEF components installed.

{domain root}/index.php/component/kunena/userid-239?func=profile&Itemid=135

Are you sure that 135 is the itemid for uddeIM component?
According to the line above 135 has been identified as itemid for com_kunena.

No, I am not 100% positive. I am just learning about itemIDs. Is there an easy way to list all of the itemids, and see what is attached to what?

I believe that uddeIM is itemID=135 because when I look in my main menu, and see what I've got linked to where, uddeIM shows 135. (See screenshot attached).

If I am looking at the numbers wrong, or if I don't understand the itemid correctly, I apologize for the confusion.

It seems to be a problem with the itemid. According to your screenshot uddeIM has I'd 135 but the link above says that Kunena has id 135. Maybe uddeIM reads the wrong itemid for Kunena.

It will take a few days to figure this out.

Ok, found the bug that uddeIM uses the wrong itemid.

Nevertheless this may not fix your problem since I tested it with a correct and wrong itemid and the profile was always shown correctly ("Kunena 2.0+" selected in integration tab).

Thanks, slabbi. Is there a solution I can try?

Also, after updating with your updated files, in the integration tab, I mentioned that the option for Kunena 3.0 appears as:
_UDDEADM_KUNENA30

This doesn't contribute to the problem, does it?