Praise be to Allah.
This hadeeth was narrated by al-Tirmithi in: Book of the virtues of the Quran, Chapter: One who recites a letter of the Quran, what reward he will have. No. 2922. Also narrated by al-Imam Ahmad in his Musnad, no. 19795
Its isnad (chain of narrators) includes Khalid ibn Tahman of whom Ibn Hajar said: He is sadooq (truthful) but was accused of being a Shi’i then he became confused.
Taqreeb al-Tahdheeb, 1644.
It was classed as da’eef (weak) by al-Albani (may Allah have mercy on him). See Da’eef Abi Dawood, 2922.
There are many thikrs (words of remembrance) for morning and evening that are narrated in saheeh (authentic) reports from the Prophet (peace and blessings of Allah be upon him). See some of them in question no. 12173.
And Allah knows best.