My wife’s just bought one too, it arrived yesterday.
It’s designed to be folded and placed in the bag it comes in, so I don’t see any issues with storing it like that. However, you must ensure it’s properly dry inside and out before storing it in that way to prevent mould build up etc.
After use, if you can, I would just hang it on a coat hanger in a cool dark dry place (after rinsing and drying of course) and just fold it for packing for travel, although placing it flat in your suitcase might actually work better...