The primary purpose of the study is to evaluate the effect of lithium at 12 weeks (capsules dosed at 62.5mg, 125mg, and 250mg), compared to placebo, on social communication deficit in patients with Phelan-McDermid syndrome. The secondary objectives of the study are to evaluate the effect of Li+ at 12 weeks on all main symptoms in patients suffering from Phelan-McDemid syndrome (PMS) including evaluating the tolerance of LI+ for 12 weeks, residual effects after stopping treatment, and parents’ feelings at the end of the study regarding the child’s behavior and impact on their daily life.