[en] The overlap of the α-t interaction times, the ₇Li wave function with the product of the α and t wave functions, and the analogous quantity for the charge-conjugate system are calculated on microscopic grounds. This quantity contains the structure information on the ₇Li nucleus in the standard finite-range DWBA description of α and t stripping from and pick-up to ₇Li. This nucleus is described in the generator-coordinate model assuming the α+t two-cluster structure and schematic nucleon-nucleon forces. The model reproduces the measured g.s. properties reasonably. The microscopic potential overlap is obtained to be very different from those calculated with using local macroscopic α-t interactions, but the difference in the ₁₂C(₇Li,t)₁₆O cross section is only dramatic at backward angles. To facilitate further DWBA analyses, several versions of the potential overlap as well as the overlap without the potential are given in an easily accessible form. (author)