Renting to a Mexican citizen living in the US

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I have a very nice couple with three well behaved kids that wants to rent one of my homes. The problem for me is trying to verify if they are good tenants or not. I asked for the standard copies of each of the couples drivers license and SS card. He provided a Mexico drivers license and ID card but nothing from the US, she had no ID at all.

He has been working as a foreman for his brother in law for over two years and he used to own a home here, they have been here over ten years. Neither of the couple speaks real good English but the wife can communicate with me if I use common words and I don't go too fast. They gave me a recent credit report in the husbands name but there was no SS number shown on it, I have a company do a full background check on my prospective tenants and they need the SS number and license for that.

I am a hard facts kind of guy, trust but verify. If I rented by the seat of my pants they would be in already. They have a newer car that is in great condition and it's clean, I also went to their little home and although it was very basic it was clean and smelled clean.

Who here has experience renting in this situation and can give me some tips that may help out others on this board.