If you are running the server on a Windows machine you can use COM to access the data in the Access db and transfer it that way (don't have a clue how, but you can).
If you are running on a Linux box you will need to export a csv file and then write a script to input the data from the uploaded csv file into your db.
If the object is to allow the client to synchronize their local db to the remote MySQL db you could use myodbc and write a macro in access to synchronize the two.
What is the objective and how much data needs to be transferred? How often?