Praise be to Allah.
It is not permissible to write the Mus-haf in anything other than the ‘Uthmaani script that was agreed upon at the time of the Sahaabah.
Ashhab said: Maalik (may Allaah have mercy on him) was asked: Can the Mus-haf be written in the scripts that the people are used to. He said: No, it should be written as it was written initially.
This was narrated by Abu ‘Amr al-Daani in al-Muqni’, then he said: None of the scholars of the ummah disagreed with that.
Imam Ahmad (may Allaah have mercy on him) said: It is haraam to differ from the script of the Mus-haf of ‘Uthmaan in ya’, waw, alif or any other letter.
Al-Bayhaqi said in Shu’ab al-Eeeman: Whoever writes a Mus-haf should adhere to the letters as they are written in these Mus-hafs and not write them differently or change anything that they wrote, for they had more knowledge and were more sincere in heart and in speech, and were more trustworthy than us, so we should not think that we know better than them.
And he narrated that Zayd said: Recitation should be done in accordance with the Sunnah. Sulaymaan ibn Dawood al-Haashimi said: This means, do not differ from the people, rather follow the Sunnah.
He said: I heard something similar in meaning from Abu ‘Ubayd concerning that, and you see that the reciters never paid any attention to the way the Arabic language is written if that differs from the script of the Mus-haf and adhering to the script of the Mus-haf is one of the established ways that no one has the right to differ from. End quote.
See: al-Burhaan fi ‘Uloom al-Qur’aan by al-Zarkashi (1/379); al-Itqaan by al-Suyooti (4/146).
Al-Suyooti (may Allaah have mercy on him) said in al-Itqaan: They are unanimously agreed that it is obligatory to follow the script of the ‘Uthmaani Mus-hafs in [rules of tajweed]. End quote from al-Itqaan fi ‘Uloom al-Qur’aan (1/250).
All of this applies if what is meant is writing the Mus-haf in full.
But when it comes to writing a verse or a few verses, and quoting them in books or magazines, and the like, there is nothing wrong with it, and this is what people do in their books, although it is better to use the script of the Mus-haf whenever possible, and to quote it directly from the Mus-haf.
The ruling on that has been explained in the answer to question no. 97741.
Based on that:
There is nothing wrong with what you have mentioned about showing some verses on the screens of mobile phones in something other than the ‘Uthmaani script, if it is not possible to show them in the ‘Uthmaani script, but one should take care to make sure than the verses that are written in this manner are those that are usually easy to read, and not subject to mistakes. And one should take care to make sure that they are written correctly so that there will be no errors in reading and publishing them.
And Allaah knows best.