The safest way to send money through the mail is through either a money order or a check.
Sending cash through the mail is allowed and possible but it's not safe because cash can easily be stolen through the mail and there is no way to trace the lost or stolen cash.
I've sent cash through the mail before and one time it arrived okay to the person and then the next time I sent cash through the mail the cash was stolen and only the envelope got the person and was taped shut.
The envelope was torn open and not just tore by machine so I assumed someone stole the cash money which was $100.00
I never got that money back so now when I send any money through the mail I send either a money order or a check.
A cashiers check would also be a good way to send money through the mail but you can buy money orders through the USPS for $1.50 and if lost you can get a refund on the money order as long as it's not been cashed.