A brother is living in the same room with his girlfriend, and he intends to observe the month of Ramadan. Should he leave the room or should continue sleeping in the same room with his girlfriend?
It is good that your friend intends to observe Ramadan as fasting this month expiates all but major sins in between two occurrences of Ramadan:
عن أبي هريرة أن رسول الله صلى الله عليه وسلم كان يقول: الصَّلَوَاتُ الْخَمْسُ وَالْجُمُعَةُ إِلَى الْجُمُعَةِ وَرَمَضَانُ إِلَى رَمَضَانَ مُكَفِّرَاتٌ مَا بَيْنَهُنَّ إِذَا اجْتَنَبَ الْكَبَائِرَ
Abu Huraira reported: Verily the Messenger of Allah (ﷺ) said: "The five (daily) prayers and from one Friday prayer to the (next) Friday prayer, and from Ramadhan to Ramadhan are expiations for the (sins) committed in between (their intervals) provided one shuns the major sins."
Yes, your friend has to leave his girlfriend's room immediately and permanently, not just during Ramadan. Adultery and fornication are major sins in Islam that Muslims should refrain from:
وَلَا تَقْرَبُوا الزِّنَا إِنَّهُ كَانَ فَاحِشَةً وَسَاءَ سَبِيلًا
And do not approach unlawful sexual intercourse. Indeed, it is ever an immorality and is evil as a way.
Assuming that your friend and his girlfriend do not get engaged in unlawful sexual intercourse, still sharing a room could result in other forms of adultery that may lead to actual unlawful sexual intercourse, and therefore this sharing of a room is forbidden in Islam:
عن أبي هريرة عن النبي صلى الله عليه وسلم قال: كُتِبَ عَلَى ابْنِ آدَمَ نَصِيبُهُ مِنَ الزِّنَى مُدْرِكٌ ذَلِكَ لاَ مَحَالَةَ فَالْعَيْنَانِ زِنَاهُمَا النَّظَرُ وَالأُذُنَانِ زِنَاهُمَا الاِسْتِمَاعُ وَاللِّسَانُ زِنَاهُ الْكَلاَمُ وَالْيَدُ زِنَاهَا الْبَطْشُ وَالرِّجْلُ زِنَاهَا الْخُطَا وَالْقَلْبُ يَهْوَى وَيَتَمَنَّى وَيُصَدِّقُ ذَلِكَ الْفَرْجُ وَيُكَذِّبُهُ
Abu Huraira reported Allah's Messenger (ﷺ) as saying. Allah fixed the very portion of adultery which a man will indulge in. There would be no escape from it. The adultery of the eye is the lustful look and the adultery of the ears is listening to voluptuous (song or talk) and the adultery of the tongue is licentious speech and the adultery of the hand is the lustful grip (embrace) and the adultery of the feet is to walk (to the place) where he intends to commit adultery and the heart yearns and desires which he may or may not put into effect.