ब्रह्ममुहूर्त और तहज्जुद।

Has Brahammuhurt been taken from Islam or Tahajjud time?

No, this Brahmamuhurat has not been taken from the concept of Tahajjud. It is prevailed in Hinduism from centuries. It is one of the most beneficial Muhurats for Yoga and Meditation as mentioned in various scriptures and as known in Hindu culture such as Manusmriti (4:92) , Bhagwat Puran (10:70:4 - Shri Krihsna used to meditate during this time) and Ashtanga Hridayam (2:1). Please see Ashtanga Hridayam which is a very famous scripture of Ayurveda written by Vagbhata. The date of this text is well before the time of Prophet Muhammad. It is a well known muhurat and mentioned in numerous scriptures and Ayurveda books. Hindu scholars are very much aware of it since it is very famous.

1. Read the Astanga Hrdayam published by Chaukhambha Publisher, the most authentic one. You will know about the Vaghbhat authorship in preface itself. Chinese traveller I-tsing (7th cent.) has stated that the Ashtnaga Hridaya was widely popular in entire India. It has also been written that the Vaghbhat had taken such knowledge and practices from the earlier great scholars.

2. Manusmriti and such Ayurveda Texts are older than Prophet. If you say this shloka may be interpolation then it may also not be the one. You can't confirm.

3. It's not just about Manu, it's mentioned in various Hindu Dharama text and ayurveda books. This muhurat is accepted as ancient practice by Hindus scholars.

4. One requires solid evidences to say that this practice was taken into Hinduism or its texts from Islam or Muhammad saw.

5. Most of the muslims out of ignorance, are not at all ready to accept this world had great civilisations, arts, practices, knowledge etc even before Islam. They think that the whole world was living in Jahiliya.  As, there was no Sanatan Dharama or Manu Smriti or Ashtang Hridayam or Ayurveda or Yoga before Prophet Muhammad and they all started after Prophet Muhammad.

आयुर्वेद के ग्रन्थों में कहा है-

ब्राह्मो मुहूर्ते बुध्येत स्वस्थो रक्षार्थमायुषः ।

(भावप्रकाश १/४)

अर्थात् स्वस्थ व्यक्ति को अपनी जीवन-रक्षा के लिए ब्रह्ममुहूर्त में उठना चाहिए।

महर्षि मनु का आदेश है-

ब्राह्मो मुहूर्त बुध्येत धर्मार्थों चानुचिन्तयेत्।

कायक्लेशांश्च तन्मूलान्वेदतत्त्वार्थमेव च।।

(मनुस्मृति ४/९२)

अर्थ:-प्रत्येक व्यक्ति को ब्रह्ममुहूर्त में उठ के धर्म और अर्थ का चिन्तन करना चाहिए।शरीर के रोग और उनके कारणों का विचार करना चाहिए।फिर वेद के रहस्यों का भी चिन्तन करना चाहिए।