ExQuilla is only officially available for normal release versions of Thunderbird, and ExQuilla will only work with versions of Thunderbird for which it has been specifically targeted. But we will occasionally release beta versions of ExQuilla that will work with beta versions of Thunderbird, particularly as Thunderbird approaches an official release (Thunderbird 45 for example is scheduled for release in March 2016).
If you want to get notices of releases of beta versions of Thunderbird that you can test, subscribe to this topic. We will post message comments here announcing beta versions of ExQuilla as they are released.
As of 2015-11-9, there are no beta versions of ExQuilla available for recent Thunderbird betas, but we hope to have a version that will work with Thunderbird beta 43 soon after that is released.