Vonny and Lance answered in no time to my query about a puppet someone I know is in the process of restoring.
I found them with a little searching in Google - and my previous knowledge of puppets - and my Dad's Dictionary of Puppets, etc. Their site looked the best informed, and displayed the highest quality of work, so I am very grateful to them for taking the time to enlighten me.
For future reference, if you have similar enquiries, they run a forum, which is probably the better way to approach a puzzle like this.
This particular character is one of the monkeys - an Anggada. Go look at the pictures of the other characters, too, and video clips, etc.