I've made some Mesh Gradients I want to copy about inside a design and into other files.

But when I copy a mesh gradient I lose all the settings and the frame returns to transparent. 

Anyone have a workflow to solve this?

The used mesh gradients appear in the "Fill and Stroke" panel like color swatches; so all you have to do is to select the new shape go "Fill and Stroke"->Fill->Mesh Fill and pick the one from the drop down.

Thanks @PixelPest, that does seem the most obvious solution.