put oneself in sb's shoes

put oneself in sb else's place AND put oneself in sb else's shoes (to allow oneself to see or experience something from someone else's point of view; to imagine that you are someone else and have to do what they do) — поставить себя на место другого (человека); представить себя на месте другого

Example 1: Put yourself in someone else's place, and see how it feels. (thefreedictionary.com)
Example 2: I put myself in Tom's shoes and realized that I would have made exactly the same choice. (thefreedictionary.com)
Example 3: Now put yourself in the place of a policeman who is afraid and has to arrest a big guy with a knife. (Cambridge Dictionary of American Idioms)

project oself into the place of sb else

Example: As far back as the eighteenth century, the Scottish moral philosopher and economist Adam Smith proposed that we project ourselves into the place of others by using our imagination, thereby entering their worlds and bodies and becoming in some sense the same person.