If in fact that case was nolle prossed or dismissed after the PTI and he doesn't have a conviction it wouldn't be a problem from an immigration standpoint. He would meet the petty theft exeption anyway since it was a misdemeanor and it sounds like he wasn't sentenced to more than 6 months in jail since he got PTI. If he got PTI I would assume he never went to jail too. To be sure you should go to an experienced immigration lawyer and bring with you copies of all the criminal documents for an opinion you can rely on.
It could. Please post your question under the immigration section so you can get some good information. Or perhaps an immigration lawyer here will answer your question.
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The INA makes removable a non-citizen convicted of a crime involving moral turpitude (CMT) committed within five years after the date of admission and resulting in a sentence of imprisonment for at least one year. The date of admission is the last date that you entered the United States before becoming a permanent resident, or the date that you became a permanent resident, whichever is earlier.
Shoplifting is considered a crime of moral turpitude. However, an alien convicted of a single misdemeanor classifiable as a petty offense is not removable. This is because the sentence that may be imposed is less than one year. This is the petty offense exception of § 212(a)(2)(A)(ii)(II) of the INA.
Recently, in the BIA decision of "Matter of Heredia-Pedroza", the court held that the petty offense exception would apply in a situation where the crime involved moral turpitude.
However, when applying for citizenship it will be necessary to show that you have been a person of “good moral character”.