MST and one Claims?

I see one claims that is FALSE.

The following is False about MST of Graph G that is a simple undirected, weighted and connected graph.

if the weight of an edge e=(u, v) is equal to maximum lightest edge in all paths between u and v then e be in the Minimum Spanning Tree.

Who can help us to see why this is FALSE. How we can say it's a false claims?

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