Can a single woman, legally divorced in Ukraine, come to USA on a tourist visa and then get married here and qualify to get a green card?

Can same woman be here on a tourist visa, then get hired, and then change her visa to H-1B to qualify for a green card?

Help please.   Mark

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Technically, when she's getting a tourist visa, she's promissing not to engage in any actiities which will lead to change of her immigrant status, but for what I know, if she gets married, INS usually will let the status change.

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