I've probably tried all user interfaces for FIBS. IMHO JavaFIBS2001 is the best! DelFibs, a new client introduced on FIBS board recently might be a strong contender.
You complain, that JavaFIBS is slow. On any normal computer, JavaFIBS should be as fast as reqired. Is it really JavaFIBS that is slow, or is it perhaps the connection (yours or that of your opponent) that is slow. In case of a slow connection, JavaFIBS can't be faster than the connection.
Very time consuming processes running on your computer might interfere with JavaFIBS (and any other application). If I run GNUBG in the background to analyze my last match for instance, this is slowing down other processes on the computer. In that case give the time consuming processes a lower priority.
With regards to your question how to invite a player to resume a match: If you select the players list window of JavaFIBS, there is a dropdown list titled "Pts:"

There you have to select "Resume". Then you select the player you want to invite in the players list and press the following button (marked by a red circle):

Often you will not see all players who are presently online in that list. You will find guidance to deal with that problem in my article
FIBS-Problem: I Can't See All Players.
Hope this helped!
Yours,
Hardy