This article shows that tree-child networks of level \(k\), where \(k \geq 2\), are determined by their MLLS. A polynomial time algorithm for recovering such a network from their MLLS is derived. In this case, one of the properties of daughter trees was used – the lowest node of the tree is in a cherry or net cherry. The obvious obstacle to this method is that there are no guarantees or reasons for obtaining a set of all MLLS of the source network. Converting sequence data to MLLS can be quite complex, especially for a higher level. To make the results practical, one can use similar approaches, for example, these are methods that work with subnets of only three leaves. However, it is not necessary to know all the MLLS to restore the original network: only three are needed. A possible application of this approach may be as follows. Assume that in different studies they created networks with some patterns. However, in each of these networks some actual mesh events were skipped, possibly due to computational limitations or lack of data. A method based on the theoretical results of this work can be used to reconstruct the entire network from networks with missing events. There is also the prospect of expanding MLLS reconstruction results for a more general class of networks. Since the authors’ ultimate goal was to determine the reconstruction of networks from their MLLS, this can be done by analysis of a similar pair of leaves, but the authors obtained results for a large number of cases, with level 2 networks containing 15 possible forms. Accounting for level \(k\) generators can provide an interesting approach to this problem.