Praise be to Allah.
We put this question to Shaykh Muhammad ibn Saalih al-‘Uthaymeen, may Allaah preserve him, who answered as follows:
If she is one of those whom it is permissible to marry, then there is nothing wrong with that, because the Prophet (peace and blessings of Allaah be upon him) said: “A woman may be married for four things” and he mentioned wealth as one of them… and this is akin to that. If he marries her in order to obtain the settlement visa, he should not have the intention of divorcing her as soon as he gets his settlement. And Allaah knows best.