I have just read your email and have to say that I was a bit overwhelmed about your file problems. I was looking into suggesting that you buy a new rack mount or a new network server, but they are tremendously expensive ranging from $1,000- $5,000. Also the time it will take for you and your employees to learn about the new server, buying it, and then installing it will be time consuming.
You also mentioned that you cannot afford too many expenses at the time being which will also affect the outcome of my suggestions. First what seems to be the only option in my opinion would be to move your business into a Cloud Server. There is a company called Dropbox and after doing some research has some great things to offer that can help out. Dropbox is a great way to store files, share files and access files from any device such as smart phones and computers. So even if you have an Apple, Windows, or Android device you can access your files from any device. Dropbox also has selective sync which is a good resource that lets you save important files to your computer or if you wish to delete them then you can also. For sharing files to the U.S office Dropbox lets you share all of your files that you wish to the people in your contacts and in your business. Whatever changes you make to the files in Timbuktu then the changes will also change in the U.S files since all of the files are in the Dropbox. You can also use the admin console that will only appear to the designated admins to the account and from hear you can invite members which will be the employees in the U.S office. There is more than I can say about Dropbox for Business and have attached a link that has even more details about Dropbox. Link- https://www.dropbox.com/business
I highly suggest investing your money into Dropbox for business as it is trusted by many high end companies as well. If you have any question or concerns please contact me at my information below.
Email- email@email.com