The purpose of the present paper is to prove a necessary and sufficient condition for a unique Einstein's connection to exist in 7 - g -UFT and to display a surveyable tensorial representation of seven-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations of the third kind obtained in earlier papers. All considerations in this paper are restricted to the first and second classes of X 7 , since the case of the third class, the simplest case, was already studied by many authors.