You can't INSERT into an auto_number field. Provided that all your auto_numbers in the original database are sequential (you didn't do any deletes) you can export all the columns in the table except the autonumber (ordering by your auto_number field), and then LOAD DATA INFILE specifying all columns except the auto_number column. If there are no "skips" in the numbering scheme, the numbers should match from one table to the other.
To make sure you haven't deleted rows in Access, check that SELECT MAX(auto_number) equals SELECT COUNT (*) from your table.
If you did deletes in Access, you could be out of luck. Your only hope would be if you can alter the mySQL table so that the identity column is not auto_number, load your data, and then alter it back so that the identity column IS auto_number. I don't know if mySQL will let you do that... check the manual under ALTER TABLE.
Here's one final trick. If you can find all the auto-generated numbers that had been deleted from the Access table, you can alter the Access table so that this column is not auto_number. Add a row for each of these missing numbers, with one of the character fields containing some unique text like "###DELETEME###". When you have completed this, then MAX(auto_number) will equal COUNT(*), and you can use the first solution I outlined above; after you are finished loading the data into mySQL, you can run a DELETE statement where that text field = '###DELETEME###'.