Abu Dawud

Benefits and Issues:
It does not befit any believer to deceive a Muslim or to covet something that belongs to another.
Similarly, it is not permissible for co-wives to create such a situation among themselves that causes the other to become distressed.
Nor is it permissible for anyone to present themselves as an ascetic (zahid) merely for show, while the reality is otherwise.

Hadith Commentary:

And to display among people that these clothes are mine—such a boastful person ultimately always becomes humiliated and disgraced. It is as if the Prophet sallallahu alayhi wa sallam did not permit even a false statement before a co-wife; this is the pinnacle of piety.

Hadith Commentary:
(1)
The meaning of "mutashabbi‘" is:
To display satiety, even though one is not actually satiated.
It is likened to clothing because both satiety and clothing conceal a person—one conceals inwardly, the other outwardly.

(2)
Some scholars have interpreted the meaning of "two false garments" as follows: a liar puts on the cloak and lower garment of an honorable man in order to give false testimony, so that the liar appears to be respectable.
Similarly, some women apply a different colored powder under their shirt so that it appears as if they are wearing two shirts.

(3)
It is a blameworthy act on the part of a woman if she, in order to provoke jealousy in her co-wife, claims that her husband has given her certain things, even though he has not given her anything.
Such a woman is like that false person who, for the sake of showing off, wears the garments of ascetics, even though he is not an ascetic.
(Fath al-Bari: 9/394)

Benefit:
In this hadith, one type of falsehood is mentioned: that a person outwardly displays something which, in reality, he does not possess. This is a lie and a major sin (kabirah). This is a general category of lying. May Allah, the Exalted, grant us the ability to avoid it. Ameen.