Durable reconstitution of the distal lung epithelium with pluripotent stem cell (PSC) derivatives, if realized, would represent a promising therapy for diseases that result from alveolar damage. Here, we differentiate murine PSCs into self-renewing lung epithelial progenitors able to engraft into the injured distal lung epithelium of immunocompetent, syngeneic mouse recipients. After transplantation, these progenitors mature in the distal lung, assuming the molecular phenotypes of alveolar type 2 (AT2) and type 1 (AT1) cells. After months in vivo, donor-derived cells retain their mature phenotypes, as characterized by single-cell RNA sequencing (scRNA-seq), histologic profiling, and functional assessment that demonstrates continued capacity of the engrafted cells to proliferate and differentiate. These results indicate durable reconstitution of the distal lung's facultative progenitor and differentiated epithelial cell compartments with PSC-derived cells, thus establishing a novel model for pulmonary cell therapy that can be utilized to better understand the mechanisms and utility of engraftment.