Summary: A certain new concept of connectedness in frames is introduced, namely, “local connectedness with respect to”. We show that whenever \(h:L\to M\) is a dense homomorphism with \(M\) locally connected with respect to \(h\), then \(h\) preserves connectedness. (This provides a “partial” converse to a result of D. Baboolal and B. Banaschewski [J. Pure Appl. Algebra 70, No. 1/2, 3-16 (1991; Zbl 0722.54031)].) Also, under the hypothesis, the right adjoint preserves pairwise disjoint joins.