 This is a phase II, open-label, nonrandomized, prospective study to evaluate the activity, safety, and feasibility of administration of moxetumomab pasudotox in the pre-allogeneic hematopoietic cell transplantation HCT setting to patients with B-lineage Acute Lymphoblastic Leukemia ALL who are in a morphologic complete remission and have pre-transplant minimal residual disease MRD 0.01 detected by flow cytometry. The primary objective of this study is to determine if treatment with moxetumomab pasudotox in the MRD positive setting is able to lead to MRD negativity 0.01 by flow cytometry or at least a 1-log10 reduction in MRD prior to allogeneic HCT. 