Learn Finnish: Onko opettajalla kartta? Hänellä ei ole karttaa. - Does the teacher have a map? She does not have a map.

This is the main rule for negative possession! In an affirmative sentence (when someone has something), the thing owned is in its basic form, like kartta. But when the sentence is negative (using ei ole), the thing you don't have must be in the partitive case. Adding -a to the end makes it karttaa.

Where is the verb 'to have' in this sentence?

Finnish doesn't actually have a verb for 'to have'. Instead, you say 'at someone is something'. You put the owner in the adessive case (ending in -lla or -llä) and use the 'to be' verb. So, opettajalla on literally means 'at the teacher is'.

Why does the first sentence start with Onko instead of Opettajalla?

To ask a yes/no question in Finnish, you take the verb, add the question particle -ko or -kö, and move it to the very beginning of the sentence. The verb here is on (is), so it becomes Onko.

Why is the ending -lla on opettajalla but -llä on hänellä?