Proof of concept: This module allows you to clone a repeater matrix item from one page to another. Currently only support for non nested items and from field to field with the same name. No max/min check and no dynamic loading via AJAX.
https://www.youtube.com/watch?v=eYX10vmQPhY
Fork this module and improve it. It would be nice if this functionality is natively supported by the repeater matrix module. But not at the moment.
I lack the time and detailed understanding of repeaters. The MatrixModule is not as hookable as needed. Especially JS-side. Here it would be nice to bring this function into the module core in cooperation with Ryan.