All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad
is His slave and Messenger.
Obedience to one’s parent is obligatory in matters that are beneficial to them, provided that no harm befalls the child as a result. In the present case, we do not see that giving your mother the phone would cause you any real harm. As for your need for it, you may give precedence to your mother in using it, thereby fulfilling her wish and bringing comfort to her heart, especially if you use it mainly for non-essential matters. Moreover, you can compensate for this by reading or by using another device, such as a computer.
As for what you mentioned regarding the Fajr prayer, it is sufficient for you to ask your mother to wake you for the prayer and explain to her that you need the phone for this purpose. If she undertakes to wake you, then the intended purpose has been fulfilled. You may also replace the phone with an inexpensive alarm clock that will wake you for the prayer, so long as your mother is in need of the phone.
In conclusion, honoring one’s parents and obeying them occupy a lofty status in the Islam. Therefore, you should not cause your mother distress or anger over this matter.
Allah knows best.