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Yes you can without too much trouble.
Assuming that you have PHPmyadmin, select all tables that pertain to the Forum and choose Export.
Now is where some options come into play. If your new forum does not have any existing post that you want to keep choose the option:
Add Drop Table (if exist)
This will drop and recreate the tables with your data entered into the tables. I am assuming that is what you are doing.
Now you may have to edit the SQL file to reflect any change in database name or prefix.
HTH.