A woman’s prayer in her house is better than her prayer in the mosque
Question

I am a married man. My wife is currently in another country visiting her family. She heard a lecture about the reward of the congregational prayers, especially Fajr prayer, and she wants to get the reward of the congregation. But she should not go to the masjid as it is at very late time? And it is also about two hours far. Will she get the same reward if she prayed it at home? Will I be considered sinful if I pray Fajr for her after I finish my Fajr prayer?.
Praise be to Allah.A woman’s prayer in her house is better than her prayer in the mosque. It was narrated from Umm Humayd, the wife of Abu Humayd al-Saa’idi (may Allah be pleased with her), that she came to the Prophet (peace and blessings of Allah be upon him) and said: O Messenger of Allah, I love to pray with you. He said: "I know that you love to pray with me, but praying in your house is better foryou than praying in yourcourtyard, and praying inyour courtyardis better for you than praying in themosque of your people, and praying in the mosque of your people is better foryou than praying in my mosque." So she ordered that a prayer-place be built forher in the furthest and darkest part of her house, and she always prayed thereuntil she met Allah (i.e., until shedied). Narrated by Ahmad (26550); classed as saheeh by Ibn Khuzaymah in his Saheeh (3/95), Ibn Hibbaan (5/595) and al-Albani in Saheeh al-Targheeb wa’l-Tarheeb (1/135). 
It was narrated from ‘Abd-Allah ibn Mas’ood (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) said:
"A woman’s prayer in her house is better than her prayer in hercourtyard, and her prayer in her bedroom is better than herprayer in her house."Narrated by Abu Dawood (570) and al-Tirmidhi (1173); classed as saheeh by Shaykh al-Albani in Saheeh al-Targheeb wa’l-Tarheeb (1/136). 
“In her house” refers to the room in which the woman is. 
“in her courtyard” refers to the central part of the house to which all the doors open. It is like what people nowadays call the hallway. 
“her bedroom” refers to a smaller room inside a larger room, where she keeps her precious belongings.  
See: ‘Awn al-Ma’bood. 
Based on this, tell your wife that this is better, and that by praying in the house she will attain a reward greater than that for praying in the mosque, praise be to Allah. 
Secondly: 
Your praying on behalf of your wife is not valid, and does not count instead of her own prayer. No one can pray on behalf of anyone else, whether they are living or dead, according to the majority of scholars, and some narrated that there was consensus on this point. See: Fath al-Bari (11/584). It says in al-Mawsoo’ah al-Fiqhiyyah (2/334): As for purely physical acts of worship, such as prayer and fasting, it is not permissible to delegate someone else to do them when one is alive. End quote. 
And Allah knows best.