The aim of this paper is to give a Boolean valued analysis approach to the theory of injective Banach lattices and establish a Boolean valued transfer principle from AL-spaces to injective Banach lattices. We prove that every injective Banach lattice embeds into an appropriate Boolean-valued model, becoming an AL-space. According to this fact and fundamental principles of Boolean valued models, each theorem about the AL-space within Zermelo–Fraenkel set theory has an analog for the original injective Banach lattice interpreted as the Boolean-valued AL-space. Translation of theorems from AL-spaces to injective Banach lattices is carried out by appropriate general operations of Boolean-valued analysis.