If one is a Christian or another religion of the books, sincerely believes in God, and refrains from the sins of his religion. Will this person be able to go to heaven?

[An-Nahl:97]:
مَنْ عَمِلَ صَالِحًا مِّن ذَكَرٍ أَوْ أُنثَىٰ وَهُوَ مُؤْمِنٌ فَلَنُحْيِيَنَّهُ حَيَاةً طَيِّبَةً وَلَنَجْزِيَنَّهُمْ أَجْرَهُم بِأَحْسَنِ مَا كَانُوا يَعْمَلُونَ

As for anyone – be it man or woman – who does righteous deeds, and is a believer most certainly We shall cause him to live a good life. and most certainly shall We grant unto such as these their reward in accordance with the best that they ever did