All perfect praise be to Allah, The Lord of The Worlds, and may his blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
It is permissible for a person to say "Allah speaks the truth" after reciting the Glorious Quran. This is meant to praise Allah, The Exalted, as He praised Himself when He Said (What means): "Say: "God speaketh the Truth: follow the religion of Abraham, the sane in faith; he was not of the Pagans."{Al-Emran/95}. It is permissible for a person to praise Allah at any time, and doing so after reciting the Quran is neither innovative nor violates Sharia.
On the contrary, it glorifies the Quran and shows politeness with Allah. Buraydah ibn al-Hasib narrated :"The Messenger of Allah (PBUH) delivered a speech to us; meanwhile al-Hasan and al-Husayn came upon there stumbling, wearing red shirts. He came down from the pulpit, took them and ascended it with them. He then said: Allah truly Said: "Your property and your children are only trial". I saw both of them, and I could not wait. Afterwards he resumed the speech." {Abu Dawud}. Ar-Ramli, a Shafii scholar, said: "If a person said "Allah Speaks the truth" after reciting some verses, there is no harm in that. "{Hashyat Nehayat al-Mohtajj, vol.2/pp.43}. And Allah Knows Best.