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Just because a company is "legit" in that it's a real business doesn't necessarily mean it's a good business. Now that being said, there are a LOT of red flags here. First of all, typically when you're contacted to sell a timeshare in Mexico (or other country) that's a massive red flag that it's a scam. 99% of the time these companies don't contact you. They can place an ad online and get more than enough people interested in selling their timeshares to contact them.
NExt, the address shows that it's for sale: http://www.trulia.com/property/3185199982-720-N-Saint-Marys-St-San-Antonio-TX-78205. Doing a search for the address does not reveal the company (which it should for a legit business). "R&R Solutions" is not a registered name with the Texas Comptrollers office.
Their website is incredibly generic, no names or photos of owners / directors / board members / etc... But most importantly the language from the website is lifted off other sites. Compare: http://www.r-rsolutions.com/in-house-closing-departament.html with http://www.mcnallyinvestmentprofessionals.com/in-house-closing-department/. Quotes:
"With experience dating back to 2002,R&R SOLUTIONS offers its services through direct operations and a network of qualified agents across the United States as well as internationally."
"With experience dating back to 2002, McNally Investment Professionals offers its services through direct operations and a network of qualified agents across the United States as well as internationally."
Note that I'm not suggesting that you go with McNally either. They could just as well be a scam, having lifted this information from another site. It could be the same operator. The point is that there's nothing that would give me any form of confidence that this was legit.
Hope that clears things up a bit. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for the time and effort that I spent on this answer unless and until you rate it positively (3 or more stars). Look for the stars on your screen (★★★★★). Thank you, ***** ***** luck to you!