If one character is grappling another, will they be pulled by a third character casting Thorn Whip?

My Fighter NPC and a Barbarian PC were prone, and the Fighter had the Barbarian grappled. A PC Druid then used thorn whip (PHB, p. 282) to pull the Fighter.

Do both the Fighter and Barbarian get pulled? Can the Druid even pull the Fighter?

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