If it were me I would:
On the Linux box you would use mysqldump to drop the db to a file. Open a command prompt and
mysqldump -u [username] –p[password] [database_name] > [dump_file.sql]
The parameters of the said command as follows:
[username] - the databases MySQL username.
[password] - the MySQL password for the user.
[database_name] - the Database name you want to take backup.
[dump_file.sql] - The name of backup dump file you want to generate. I usually use databasename_YYYYMMDD.sql.
On the windows server install MYSQL Workbench (from mysql). Transfer the .sql file you created from the Linux box to the Windows box. Launch MySQL Workbench, connect to the MySQL instance, and then click import. Select the file. (see MySQL workbench documentation or Google for more information.)
