The development of the Internet of Things (IoT) combined with the emergence of federated learning (FL) makes it possible for mobile edge computing (MEC) to gain insight from physically separated data without violating privacy or burdening communication and the server. Due to the distributed nature of MEC, researchers have uncovered that the FL is vulnerable to backdoor attacks, which aim at injecting a subtask into the FL without corrupting the performance of the main task. However, the single-shot backdoor attack in the early training stage is weak. In this paper, we strengthen the early-injected single-shot backdoor attack by using information leakage. We show that FL convergence can be expedited if the client's dataset mimics the distribution and gradients of the whole population. Based on this observation, we propose a two-phase backdoor attack, which includes a preliminary phase for the subsequent backdoor attack. Benefiting from the preliminary phase, the later injected backdoor achieves better effectiveness, as the backdoor effect is less likely to be diluted by normal model updates. Numerical experiments show that the proposed backdoor outperforms existing backdoor attacks in both success rate and longevity, even when defense mechanisms are in place.