[janeseymore09092]

As for the point your friend raised when he said about verse 36:12 that we cannot use the word imam and Book interchangeably, aside from what i told you above that Allah enumerated and recorded in a book not a Human, your friend needs to remember that the Quran and Arabic in general is an eloquent tongue and we understand Arabic based on how our ancestors understood it, for example in the Arabic dictionary "Lisan al-'Arab" we read:

قال الأَخفش: جُعلت الهمزة ياء لأَنها في موضع كَسْر وما قبلها مفتوح فلم يَهمِزُوا لاجتماع الهمزتين، قال: ومن كان رَأْيه جمع الهمزتين همَز، قال: وتصغيرها أُوَيْمة، لما تحرّكت الهمزة بالفتحة قلبها واواً، وقال المازني أُيَيْمَة ولم يقلِب، وإِمامُ كلِّ شيء: قَيِّمُهُ والمُصْلِح له، والقرآنُ إِمامُ المُسلمين، وسَيدُنا محمد رسول الله، صلى الله عليه وسلم، إِمام الأَئِمَّة، والخليفة إمام الرَّعِيَّةِ، وإِمامُ الجُنْد قائدهم. "And the Quran is the Imam of the Muslims, and the Prophet SAWS is the Imam of the Aimmah, The Caliph is the Imam of the subjects(citizens), The Imam of the soldiers is their general(leader)."

I add and the Imam of the prayer is the one who leads the Muslims in prayer.

It also says in Lisan al-'Arab:
الإِمامُ الخَيْطُ الذي يُمَدُّ على البناء فيُبْنَي عليه ويُسَوَّى عليه سافُ البناء "The Imam is the rope extended for construction of a building..."

and it says:
والإِمامُ الطريقُ.
وقوله عز وجل: وإِنَّهما لَبِإِمامٍ مُبينٍ And the Imam means the road. So when Allah said: ((So We took retribution from them, and indeed, both [cities] are on a clear highway.)) [15:79] In the transliteration it is "La bi Imam-min Mubeen." a clear road.

قال الفراء: وإِنهما لَبِإِمامٍ مُبين، يقول: في طَريق لهم يَمُرُّون عليها في أَسْفارِهم فَجعل الطَّريقَ إِماماً لأَنه يُؤم ويُتَّبَع.
والأَمامُ بمعنى القُدّام. And Allah called the road an Imam because as we explained before, the Imam is everything which is followed, since humans follow the road then it is called an Imam.

In "Maqayees al-Lugha" we read:
والإمام كلُّ من اقتُدِي به وقُدِّم في الأمور. "The Imam is everything whose example is followed and is placed before all else in any matter."

Which is why the Quran is called an Imam because it is followed and placed before all else, and the preserved tablet is an Imam as it has recorded the destiny and it is placed before all events.