Sending a ring by mail to Japan from USA?

Hello

I would like to mail a ring to my girlfriend in Japan, as a present.
It is gold and has some diamonds on it.
Do you think it would be a good idea to send it through the mail system to her?
Will customs be able to see it in the enevlope? Do you think there is a good chance of it getting stolen?
Would she have to pay customs for it? I bought it for $300.

The safest would be to send it via Global Priority International (they have a flat-rate small box), with insurance, if you want to, and on the little customs declaration form, mark it as "gift," and write the correct value (if you insure it). She might have to pay a small duty upon receipt, but it's better than getting it lost and not being able to even track it or recover the value.