Customs duty

Rough stone could mean anything, such as a piece of rough sandstone or limestone or a piece of fossilized coral. Or are you talking about an unpolished gemstone like an unpolished semiprecious stone? Or are there more than one?

Yes theoretically that rule should apply, value less than USD500, and if you have the receipt with value and the permission then I do not see why there should be any problem bring the stone back in. Hopefully you will not have any problems from naughty customs officers.

Take into account most values and exemptions are only permissible for 12 months maximum with the value you state on paperwork you should? Be ok but most documents with permission expire after a short period the $500 rule won’t be a concern for you due to the fact you currently own this so therefore considered your personal property (like shoes socks laptop watch etc)
Just to add your current paperwork maybe ok if you take out again you may need to check that one out

If you want to bring goods from Indonesia and brought back to Indonesia The procedure should be when you want to be taken out report Customs (there are notes) So when goods from Indonesia are brought back to Indonesia, then the notes when they leave are shown to Customs when they arrive at the Indonesian airport.