If you are unable to or don't want to use WordPress' built-in updater it's possible to update Fonts Plugin Pro manually.
Once logged in, click View Details and Downloads.
Click the file name to download it to your computer.
Inside /wp-admin navigate to Plugins → Add New and click Upload Plugin.
On the next screen choose the fonts-plugin-pro.zip file you just downloaded and click Install Now.
WordPress will inform you that the old version will be overwritten.
Click Replace current with uploaded and the process should complete successfully.