The Woman Who Is Examined - 60:10
O you who believe, when believing immigrant women take refuge with you, question them. Allah knows their faith very well. If you realize that they are believers, do not send them back to the disbelievers. They are not lawful for those disbelievers, nor are they lawful for them. Give back to them their marriages which the disbelievers have spent. There is no harm in your marrying them if you have paid them their mahr. Do not keep unbelieving women in your charge. You may ask them for the rasham you have spent on them, and they may ask for the rasham they have given you. This is the judgment of Allah. He judges between you. Allah is All-Knowing, All-Wise.
The most important criterion of belief:
The Cattle/6:82
Those who believe and do not mix their faith with wrongdoing, they deserve security and they have found the truth.
Luqman/31:13
"When Lokman advised his son, he said: "My dear son, do not associate partners with Allah; surely shirk (associating partners with God) is a great wrong."
The Companies/39:65
It has been revealed to you and those before you that if you associate partners, all that you do will be in vain and you will be of the losers.