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*For mac/OSX*
- couldn't load .swf file in chrome/safari, it would just download (copying) the file
- couldn't embed the .swf file in an .html file: whether or not I used the full pathname, or just the filename, putting the .html file in the same folder as the .swf... Chome would give me a flash error, "It may have been moved or deleted.", and safari would load a blank page.

Solution for me was to download Adobe's Flash Player Projector (for mac), available here:
https://www.adobe.com/support/flashplayer/debug_downloads.html

and load the .swf file using that.

Here is the direct link:

https://fpdownload.macromedia.com/pub/flashplayer/updaters/32/flashplayer_32_sa....

It is strange because, for me,  I take the file and put it on a window of safari  , then I keep it in the favorites.

I play it without problem, and when I want to quit (to keep the position) I go to the menu and then I can go to another page of the web or quit safari.

When I come back to the game a day after I click the favorite submachine, and I retrieve the last position.

But your solution must also be ok... ;)