The Messenger of Allah ﷺ used to remember Allah at all times.
حدثنا خلف بن الوليد حدثنا يحيى بن زكريا بن أبي زائدة عن أبيه عن خالد بن سلمة المخزومي عن البهي عن عروة
كان رسول الله ﷺ يذكر الله عز وجل على كل أحيانه
Its isnad is sahih. Khalid bin Salama Makhzumi is trustworthy, and his hadith appears in Muslim and the Four Sunan. The hadith was narrated by Bukhari 1/407, before number 305, as a suspended narration in the chapter on menstruation, and by Muslim 1/282, number 373, in similar fashion, and by Abu Dawud 1/5, number 18, and Ibn Majah 1/110, number 302, both in the chapter on supplications, and by Tirmidhi 5/463, number 3384, in the chapter on supplications.