I suggest you buy a book which compares Islam and Christianity; research books and get the one you think is best. If your mother knows you have converted to Islam, maybe you guys can read it together, or you can ask her to update you on how much she's read.
But remember, she is very likely to be extremely set in her thinking and you should not push her lest your relations with her deteriorate. Do not even argue about anything. Just state what you think and if she doesn't agree let it be. You're praying to Allah, and that's all that will change anything; only He can guide and show us the straight path.
The Quran says in (5) Surah Al-Ma'idah:
'82. Verily, you will find the strongest among men in enmity to the believers (Muslims) the Jews and those who are Al-Mushrikun (see V.2:105), and you will find the nearest in love to the believers (Muslims) those who say: "We are Christians." That is because amongst them are priests and monks, and they are not proud.
83. And when they (who call themselves Christians) listen to what has been sent down to the Messenger (Muhammad ), you see their eyes overflowing with tears because of the truth they have recognised. They say: "Our Lord! We believe; so write us down among the witnesses.
84. "And why should we not believe in Allah and in that which has come to us of the truth (Islamic Monotheism)? And we wish that our Lord will admit us (in Paradise on the Day of Resurrection) along with the righteous people (Prophet Muhammad and his Companions)."
85. So because of what they said, Allah rewarded them Gardens under which rivers flow (in Paradise), they will abide therein forever. Such is the reward of good-doers.'
But please don't forget, whoever Allah guides none can misguide, and whoever He allows to fall astray, none can guide them aright.
My prayers are with you!