Can a Shia boy marry a Sunni girl, according to the Sharia laws?
There is a Sunni girl that I know who really likes a Shia boy, and he likes her too. She was asking me today if it is permissible or restricted for this marriage to take place.
Generally, everyone should refer to his/her sect orders/Fatwas(rulings), and I'm not so familiar with Sunni viewpoint about it, but it doesn’t matter for a Shia boy to marry a Sunni girl. Because Shias consider Sunnis as Muslims, then this is permissible for a Shia male to marry a Sunni girl according to Islamic laws (Sharia) as the viewpoint of Shia.
Some Shias believe in Kufr therefore it is important to ask about the Shia individual's beliefs before marriage because:
"A woman is married for four reasons, her wealth, lineage, status and Deen. Choose the one who is religious." (Sahih al-Bukhari)
Deen (belief) has the highest priority in marriage, so it is important to ask a Shia if s/he believes the Quran has been altered for example, because many of them do.
It is important to ask a Shia whether s/he believes Angel Gabriel made a mistake when delivering the revelation for example, because many of them do, they say that the revelation was actually meant for Ali bin Abi Talib instead of prophet Mohammad.
It is important to ask a Shia whether s/he believes in Ali bin Abi Talib being God, or the son of God, or an image of God, or the trinitarian belief in Allah/Mohammad/Ali etc. Shia Allawis believe in such Kufr.
The point being, it is an individual responsibility to not paint all Shias with one brush, rather to distinguish those who believe in Kufr, and those who don't, specially when one is considering marriage.
In the name of Allah, the most compassionate, the most merciful
Firstly it could be constructive for you to know concerning a similar view of the holy Quran regarding the mentioned issue. The holy Quran terms some groups of people who you are not allow to get married to them such as Mushriks (polytheist)... Therefore you’d better look at the following verse as a beneficial related verse (al-Baqarah:221):
وَلَا تَنكِحُوا الْمُشْرِكَاتِ حَتَّىٰ يُؤْمِنَّ ۚ وَلَأَمَةٌ مُّؤْمِنَةٌ خَيْرٌ مِّن مُّشْرِكَةٍ وَلَوْ أَعْجَبَتْكُمْ ۗ وَلَا تُنكِحُوا الْمُشْرِكِينَ حَتَّىٰ يُؤْمِنُوا ۚ وَلَعَبْدٌ مُّؤْمِنٌ خَيْرٌ مِّن مُّشْرِكٍ وَلَوْ أَعْجَبَكُمْ ۗ أُولَـٰئِكَ يَدْعُونَ إِلَى النَّارِ ۖ وَاللَّـهُ يَدْعُو إِلَى الْجَنَّةِ وَالْمَغْفِرَةِ بِإِذْنِهِ ۖ وَيُبَيِّنُ آيَاتِهِ لِلنَّاسِ لَعَلَّهُمْ يَتَذَكَّرُونَ ﴿٢٢١
And do not marry polytheistic women until they believe. And a believing slave woman is better than a polytheist, even though she might please you. And do not marry polytheistic men [to your women] until they believe. And a believing slave is better than a polytheist, even though he might please you. Those invite [you] to the Fire, but Allah invites to Paradise and to forgiveness, by His permission. And He makes clear His verses to the people that perhaps they may remember. (221)
According to the viewpoint of the scholars and Marja’-al-Taqlids of Shia (whereof a part of the issue is related to a Shia boy (as a related matter)): it is permissible for a Shia boy to get married to a Sunni girl. Then you can inform them that it is allowed from the view of Shia for Shia boys to get married to Sunni girls.