Praise be to Allah.
The best with regard to reading or reciting Qur’an is that which will increase a person in focus of mind. If he will have more focus of mind when he recites from memory, then that is best. If he will have more focus of mind when reading from the Mus-haf or from his mobile phone, then that is best.
An-Nawawi (may Allah have mercy on him) said in al-Adhkaar (p. 90-91):
Reading Qur’an from the Mus-haf is better than reciting from memory. This is the view of our companions, and it is the well-known view among the early generations (may Allah be pleased with them). But this is not absolute; rather if a person can reflect, ponder and focus more when he recites from memory than when he reads from the Mus-haf, then in his case reciting from memory is better. If both options are equal in that regard, then reading from the Mus-haf is better. This is what the early generations meant when discussing this issue. End quote.
Some da‘eef (weak) hadiths were narrated from the Prophet (blessings and peace of Allah be upon him), which are not sound enough to be taken as evidence, concerning the virtue of looking in the Mus-haf. For more information on that, please see the answer to question no. 32594.
Shaykh Ibn Baaz (may Allah have mercy on him) was asked: Is there a difference in reward between reading Qur’an from the Mus-haf or reciting from memory? If I read Qur’an from the Mus-haf, is it acceptable to read with my eyes only or must I also move my lips? Is it sufficient to move the lips, or must there also be some sound?
He replied: I do not know of any evidence to suggest that there is a difference between reading from the Mus-haf or reciting from memory; rather what is prescribed is to reflect and focus, whether one reads from the Mus-haf or recites from memory. It can only be called recitation if it can be heard; it is not sufficient just to look with the eyes, or to think of the words without uttering them. The Sunnah is for the reader to utter the words and reflect, as Allah, may He be glorified and exalted, says (interpretation of the meaning):
“[This is] a blessed Book which We have revealed to you, [O Muhammad], that they might reflect upon its verses and that those of understanding would be reminded”
“Then do they not reflect upon the Qur'an, or are there locks upon [their] hearts?”
If reciting from memory will help one to focus more and reflect more on the Qur’an, then that is better; if reading from the Mus-haf will help one to focus more and reflect more, then that is better. And Allah is the source of strength.
End quote from Majmoo‘ Fataawa ash-Shaykh Ibn Baaz (24/352).
Thus it will become clear that if you read Qur’an from your mobile phone with focus and reflecting on the meaning, your reward will not be less than that for reading from the Mus-haf, in sha Allah. What matters is focus of mind and benefitting from reading Qur’an.
And Allah knows best.