But closer every day
鳩居鵲巣
kyuu.kyo.jaku.sou
Literally: dove – sit/be [in a place] – magpie – nest
Alternately: Taking someone else’s achievements or social position for yourself. Undeservedly stealing someone else’s laurels or spotlight.
Notes: This comes from our friend, the Classic of Poetry (Japanese 『詩経』 = Shikyou). The magpie is supposedly an especially good nest-builder, and the image is of its labor being taken by a bird thought to be especially bad at the task.
Apparently the original usage of this metaphor was mainly applied to a man’s social status and household being taken over by the woman who came to be his wife, but modern usage has been generalized into something less sexist. In a sort of halfway point, it can also apparently refer to someone living temporarily in someone else’s home.
The parts can be reversed to give 鵲巣鳩居. Another version uses this order but replaces 居 with 占 (sen, “occupy”) as its final character.

Pigeons can apparently be… very bad at nest-making. From Reddit.