It is well known that each STS(15) with a sub-STS(7) is derived. In this article, we will improve this result by showing that each non-simple sloop L of cardinality 16 with any possible congruence lattice C(L) can be extended to a non-simple SQS-skein S of cardinality 16 with all possible congruence lattices for C(S). Accordingly, we may say that any triple system STS(15) with m sub-STS(7)s is a derived triple system from an SQS(16) having n sub-SQS(8)s for all possible non-zero numbers of m and n.