Its actually really easy and the repair works a charm (it will also work on larger speakers).
The trick is good old elders glue and single ply toilet paper. A paper towel will work as well, just be sure to separate the ply... it needs to be thin.
In this picture, I've mixed some elmer's glue with warm water.

In this picture, I've mixed some elmer's glue with warm water.



There. That's better.

Wet each wrinkle again to make sure it lies as flat as possible. I've never had trouble with a wrinkle... it's mostly the edges that create issues.... still, it looks nicer if laid perfect. This speaker will be hidden when placed inside the radio case.
***
Now we just let her dry.

