Let's say a Shia boy married a Sunni girl according to Sunni law, then the Shia boy wants to divorce his Sunni wife.
Under which law will he give talaq? That is, by which law the talaq will be governed?
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If they live in a country that is ruled according to Sharia then, they will be ruled according to the law of that country.
If they live in a non-Muslim country then, they should follow the ruling on which they both agree upon. If they disagree with each other then, they should divorce according to the Qur'an and Sunnah.
Divorce according to the Qur'an :
The Divorce (Surat at Talaq)
In the name of Allah, the Beneficent, the Merciful.
[65.1] O Prophet! when you divorce women, divorce them for~ their prescribed time, and calculate the number of the days prescribed, and be careful of (your duty to) Allah, your Lord. Do not drive them out of their houses, nor should they themselves go forth, unless they commit an open indecency; and these are the limits of Allah, and whoever goes beyond the limits of Allah, he indeed does injustice to his own soul. You do not know that Allah may after that bring about reunion.
[65.2] So when they have reached their prescribed time, then retain them with kindness or separate them with kindness, and call to witness two men of justice from among you, and give upright testimony for Allah. With that is admonished he who believes in Allah and the latter day; and whoever is careful of (his duty to) Allah, He will make for him an outlet,
[65.3] And give him sustenance from whence he thinks not; and whoever trusts in Allah, He is sufficient for him; surely Allah attains His purpose; Allah indeed has appointed a measure for everything.
[65.4] And (as for) those of your women who have despaired of menstruation, if you have a doubt, their prescribed time shall be three months, and of those too who have not had their courses; and (as for) the pregnant women, their prescribed time is that they lay down their burden; and whoever is careful of (his duty to) Allah He will make easy for him his affair.
[65.5] That is the command of Allah which He has revealed to you, and whoever is careful of (his duty to) Allah, He will remove from him his evil and give him a big reward.
[65.6] Lodge them where you lodge according to your means, and do not injure them in order that you may straiten them; and if they are pregnant, spend on them until they lay down their burden; then if they suckle for you, give them their recompense and enjoin one another among you to do good; and if you disagree, another (woman) shall suckle for him.
[65.7] Let him who has abundance spend out of his abundance and whoever has his means of subsistence straitened to him, let him spend out of that which Allah has given him; Allah does not lay on any soul a burden except to the extent to which He has granted it; Allah brings about ease after difficulty.
[65.8] And how many a town which rebelled against the commandment of its Lord and His apostles, so We called it to account severely and We chastised it (with) a stern chastisement.
[65.9] So it tasted the evil result of its conduct, and the end of its affair was perdition.
[65.10] Allah has prepared for them severe chastisement, therefore be careful of (your duty to) Allah, O men of understanding who believe! Allah has indeed revealed to you a reminder,