Can I submit purchases on behalf of other people?

Yes, you can.

Users need 'privileged' user permissions to submit purchases on behalf of other people, or be a finance team member.

This permission is set in the user settings screen under each user's Purchase options.

By default, when submitting expenses, the payee will be the user submitting the expense. But this can be changed to another person.

To help you better understand the Purchasing module as a whole, please visit the module overview page here.