Is there a phrase to say that someone's hidden intentions are revealed in his/her talk or movements?

Solution 1:

I would say:

he's showing his true intentions

or use the following idioms:

show somebody's true colors
reveal somebody's true colors

Solution 2:

In gambling circles, this is referred to as a "Tell". For instance, if one poker player notices that another player scratches his face when he is nervous or bluffing, the first player has identified the second players "Tell". This is a slang term that refers to something the second player is doing that "tells" a different story than the one he wants you to believe. A "Tell" can be a nuance in body language, a gesture, a tone of voice, or any other subtle indicator one person has identified in another. It's a signature action that is "telling" you something contradictory to what the person is actually saying.

Solution 3:

The closest English phrase in form is

His mask is slipping.

Solution 4:

I'd go with "To belie one's stated intentions".

From the Collins English Dictionary (via thefreedictionary.com):

belie [bɪˈlaɪ] vb -lies, -lying, -lied (tr)

to show to be untrue; contradict

to misrepresent; disguise the nature of the report belied the real extent of the damage

to fail to justify; disappoint [Old English belēogan; related to Old Frisian biliuga, Old High German biliugan; see be-, lie1] belier n Collins English Dictionary – Complete and Unabridged © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003

For example, "He was kind and considerate to Angela, telling her that he simply liked her for her charming conversation and did not think of her in a romantic way, but the frequent, hungry darting of his eyes to her body belied his stated intentions."

Solution 5:

Je ne connaissais pas cette locution, mais en anglais c'est peut-être Truth will out.