You would need to go from Access to SQL Server as they both have almost the same schema were as mySQL (which is not as good as SQL Server) has a very different schema.
MS Access has a built in upsize wizard which can upsize your database to SQL Server. You should give this ago at upsizing the database.
However, we do allot of these Access to SQL Server Migrations as part of our Migration service when people move their Web Wiz Forums hosting to us and from experience I can tell you that it often takes 30 minutes to 6 hours to do, and thats for engineers who know the database inside out.
You may want to have a look at transferring your forum hosting to us and have us upsize the database for you to SQL Server. The prices are very competitive and you may find it cheaper than paying for a SQL Server database from your present host.
More information is on the page below:-
http://www.webwiz.net/webhosting/web_wiz_forums_hosting.aspThe Premium Brand Free Edition is included and upgrades are also done for you for free.