The left-arm bowler, who served a five-year ban for spot-fixing at Lord's in 2010, took the final wicket in Pakistan's 75-run win over England on the same ground.
"It's going to be a really memorable game of his life. From here he can restart his career and prove to everybody that he is a good kid now and a mature cricketer, Misbah was quoted as saying by BBC on Sunday.
Amir, 24, also served a jail term for his part in a plot with fellow pace bowler Mohammad Asif and captain Salman Butt to deliberately bowl no-balls in the final Test of Pakistan's last tour of England.
With his first Test back coincidentally coming at Lord's, Amir took three wickets across both innings, bowling Jake Ball to seal a victory that puts Pakistan 1-0 up in the four-match series.
"Everyone believes he's such a great cricketer and fine bowler and wants him to be in the game," said Misbah, whose side has now won six of their past seven Tests against England.
Chasing 283 to win, England were bowled out for 207 on the fourth evening as leg-spinner Yasir Shah claimed 4-69 to finish with match figures of 10-141.
"I am really proud of the team, the way that they fought," said Misbah, who made 114 in Pakistan's first-innings 339 -- in a match when only two other batsmen reached 50.
"Mentally everyone was strong. It was a really good win for us. Winning this Test match against a top side who are really good in their home conditions, that speaks volumes about this team and for all of the players, the 42-year-old concluded.
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