The spell Project Image creates a shadowy duplicate that the caster can use to deliver spells.
If you desire, any spell you cast whose range is touch or greater can originate from the projected image instead of from you. The projected image can't cast any spells on itself except for illusion spells. The spells affect other targets normally, despite originating from the projected image.
If the caster loses line of effect by teleportation, then the spell ends.
If you use dimension door, teleport, plane shift, or a similar spell that breaks your line of effect, even momentarily, the spell ends.
What happens if, using the shadowy duplicate as the spell's origin, you cast a teleportation spell that targets other creatures? Does the Project Image effect end immediately, thereby preventing the teleportation effect from happening? Or does the teleportation effect happen first, and then the image goes away?
Bob the barbarian is in melee combat, and in trouble. Alice the wizard is a safe distance away, and she sends her shadowy duplicate over to him. On Alice's next turn, she casts Dimension Door from the projected image, in attempt to touch Bob and bring him to Alice's location.
Does the projected image immediately disappear, leaving Bob stranded in the front lines? Or, does the image disappear once the Dimension Door has taken effect, i.e., once Bob has been teleported to Alice's location?