This work considers the problem of planning how a fleet of shared electric vehicles is charged and used for serving a set of reservations. While exact approaches can be used to efficiently solve small to medium-sized instances of this problem, heuristic approaches have been demonstrated to be superior in larger instances. The present work proposes a large neighborhood search approach for solving this problem, which employs a mixed integer linear programming-based repair operator. Three variants of the approach using different destroy operators are evaluated on large instances of the problem. The experimental results show that the proposed approach significantly outperforms earlier state-of-the-art methods on this benchmark set by obtaining solutions with up to 8.5% better objective values.