What exactly do you want? I haven't paid much attention to '02+. From what I know based on 1st and 2nd gen Explorers ('91-'94,'95-'01).
There are three transfer cases used over those years.
1) BW13-54 was used in '91-'94 Explorers and '91-'97 Rangers. For comparison, the 13-54 is essentially the same as the 13-50 in your BII with a few minor internal modifications and a different front output.
2) BW4405 was used in '95-'01 V6 Explorers, and, I think, '98+ Rangers. BW4405 is a lot like the 13-54, only with a 4Auto setting. '95-'96 have 2H, 4A, 4L settings and are accompanied by a vacuum operated front differential lock. '97+ have 4A, 4H, and 4L settings without the front differential lock.
From what I understand, the 13-54 and 44-05 share the same bolt patterns and such and will mechanically bolt up in place of each other up to '01. If nothing has changed in the 5R55E between '01 and '06, I expect you'll be able to bolt up a 4405 to your Ranger.
Being an engineer, I sometimes get carried away with defining terms exactly, but I don't like to use the term AWD to refer to the 4405. AWD to me refers to a t-case that can vary power from front to rear, but doesn't lock and doesn't have a low range. The 4405 does have a low range, and, depending on year, has a 2H or 4H option. The 4A setting on the 4405 is an AWD setting, but the other settings are also present. I suppose one could install the 4405 and it's electronics with the 4A setting selected and not put a switch on the dash.
the Bw4404 was used in 5.0 V8 applications, and is what I would call an AWD t-case. It can vary power from front to rear as needed, but doesn't allow for any user input, and can't be locked nor does it have a low range. The 4404 fits behind the 4R70W used in the 5.0 V8 applications, and doesn't fit behind the 5R55E.
I've never heard of the BW 4410 mentioned in the other thread, so I don't know what applications used it, nor what it is.
If your 5R55E (in 4WD form) is the same as a late '90's 5R55E, then you should be able to bolt up the 4405 to it. But, the 4405 doesn't sound like it's exactly what you're looking for. Someone who knows 3rd gen Explorers may know if Ford ever designed an AWD t-case (like the 4404) to fit behind the 5R55E. That sounds like what you want.
Sorry I couldn't be of more help.