score:4
You can mail a 50 pound (22.6 kg) package from the US to Japan for $180 via Priority Mail International. The maximum allowed length is 60", and the maximum length plus girth combined must be less than 108".
If you buy the postage online it is $160, and you fill out and print the customs forms at the same time. The catch is you have to get a special customs envelope that the postage label and customs forms go into; you can have these shipped to you for free or you may be able to obtain them at a local post office. If you've printed the postage and customs form online and placed them in the customs envelope, you can even have the USPS pick up the package at your home for free.
And of course the price will vary depending on the weight of the package, so you should weigh it on a reasonably accurate scale before you mail it. This service has a weight limit of 66 pounds (30 kg) per package.
Upvote:0
The cheapest is likely for her to get an extra suitcase and carry it back with her. Even at the elevated prices, it'll still be cheaper than airmail.