Hi LucyH, and welcome to a wonderful forum!
You can use the same method with mature coconut flesh as you would for dried/dessicated coconut. (I've described it near the bottom of
this page on my blog.)
You use 3 times the weight of fresh coconut flesh, broken into pieces, brown skin removed.
Weigh in 100 - 300 g fresh coconut and grate at speed 8, till fine. Then add 3 times that weight in water, cook for 5-20 minutes at 100C, speed 4 (depending on volume) until steaming. Continue with the method as described
here.
So basically, if you are starting with 300 g. fresh coconut, you would add 900 g. water and cook it for 20 minutes before proceeding. This method is described in good detail in the "Fast and Easy Indian Cooking" book from Thermomix UK.
Hope this helps cuz you will be thrilled at making your own!
Have fun
ps - OMG, thanks Judy! I just saw your link
after writing my answer. D'OH, it helps to read, doesn't it?