As the title, is there a way to easily import an old IPB database into a fresh install of IPS using the built in converter?

 

I do not see in the list the option of IPB which is weird to me.

Why are you running the converter instead of the upgrader?

Edit your conf_global.php to point to the 3.x version, and then go to domain.com/admin/upgrade and let it work through your upgrade.  

MAKE A FULL BACKUP OF YOUR DATABASE BEFORE YOU DO THIS.  

As Randy mentioned, you would not be using a converter here, you would use the upgrade. Please see: