connect joomla website

What do you mean for "connect"?

Do you mean having the same login details for both, so when a member join Dolphin is automatically subscribed in Joomla! too?

There was such modification in the past.

If many of you are interested in such modification I can create one.

This should not be very simple to realize and it may take a while, especially for the different way of storing credentials in the DB and for the different encryption.