All you need is a copy of the receiving ffl. Go to this sight,
https://www.atfonline.gov/fflezcheck/fflSearchDisplay.do , follow the instructions to make sure the FFL is legit, C&R is different. Box and ship your package through USPS or UPS, I use USPS. I do all my shipping online, I pay for the postage and print it out. Walk it into your post office and hand it to them. Go home and watch TV.
Make sure the package is sent with NO ammunition, if it is the receiving FFL is legally obliged to call the BATF and you will have a knock on your door. Only send it with adult signature, if you do not some idiot post man will leave it on the back door. Make sure the FFL has a contact name to call. You can do it the exact same way through UPS, I just use USPS because the PO is a 30 second drive from my house and the UPS is 20 minutes. Insurance is your option with USPS, buy why take the chance.
USPS requires that you bring the box in to have the post master check it to make sure it is unloaded. I do not do that, I do not want anyone to know what I am shipping. You cannot purchase shipping from one of the UPS stores, the stores all over the place, they are NOT UPS, they just bought the naming rights, they will not ship ammo or firearms through them, they do not check if you just walk in and drop off a package, however

It is very easy, I do it a lot. Once you figure out the basic laws it is super easy, just like shipping a car part.