I have been looking for an alternative service to Bettween for a while now. Bettween stopped operating a while ago.
Discovered Conweets yesterday. It is pretty similar to Bettween in terms of functionality though there are more ads.
I guess as long as the service is sustainable because of these ads, it could be considered as a necessary evil.
Like Bettween, Conweets lets you track conversations between two Twitter handles in the recent times.
It comes handy when you want to search for your own conversations from the past with a Twitter contact. Twitter makes it very hard to search for older tweets.
You can also do the same with public figures and see what kind of interactions they have with others on the Twitter platform.
The service does not seem to offer any embedding tools which is a disappointment.