it can be that groups I am member off don't interest me to put new links in all the time and that my own groups are more private.
Seeing all the groups together is a bit confusing. Seperating them would be better

when you have made a list during something happening, example ashes for the vulcanic stories, and after a while you don't use that list anymore and you want to shorten the number of lists, than you may want to transfer all the links in that list to another list, say science and nature.

I don't see how this is possible today.
I could become possible by adding a new function in the more

in which you click on all or some of the links and than on 'transfer to list' after which opens the list of lists and you chose the list

would be great