If your mother (or anyone else) has at least $500K to invest, and would like an immigrant visa, there are special EB5 programs that they can participate in. (Miami recently got special designation!)
If the investment is less than $500K or they do not want/need a visa, then you can go through the usual real estate process.
When it comes time to sell, you will be subject to the requirements of FIRPTA. Basically money will be held in escrow until you can demonstrate that you have paid any required capital gains taxes.
Keyes Real Estate