Mollet joins Edelman next week, reporting to practice MD Susan Eastoe.
He leaves F-H (formerly GPC International) after three years, working for clients such as National Air Traffic Services, DHL and Tata Consultancy Services.
A formal Royal Naval officer, Mollet first became a consultant for Ludgate Public Affairs.
He was then manager of the national public affairs team at PPS Group.
F-H meanwhile has promoted PA associate director Claire Ashbridge-Thomlinson to a director and Scott Colvin and Gavin Megaw to senior consultants.