It has happened to most music teachers with an online presence of any type. You've been contacted from abroad by a conscientious parent wanting their child to take [your instrument] lessons with you while they're in [your city] for the summer.
You find it slightly unusual that they want "Johnny" to have lessons 4 days a week for 2 months, but you would be happy to fill so many timeslots.
Even better, they really want to pay you the full amount in advance and will wire you a check tomorrow. The idea of receiving a sizable amount of money may be tempting. Should you reply and find out more?
There is always a chance it is a legitimate inquiry so you may want to reply and see how it goes. Be very cautious and do not give out any personal information like your address. If anything about the exchange makes you uncomfortable at all, politely tell them that you cannot accept payment in advance for lessons, or better yet, don't reply at all. If they are in fact a scammer, they will move on to other potential victims.
Check out the links below for more information on how to spot these types of scams and report the scammers to their email providers.