What is the way to overcome laziness in performing Fajr prayer on time, and delaying the performance of other prayers when outside the home, especially after moving to live in an Islamic country?

My advice to you is to fear Allah, be mindful of His constant watch over you, and remember that you will be held accountable for every action. Your problem is not a lack of knowledge, but rather a weakness in your heart's mindfulness of Allah. The cure for this is to reflect upon Allah's names and attributes, His rewards, and His punishments. Ask yourself, what if death were to overtake you right now? How would you meet Allah? Increase your remembrance of death, associate with the righteous, and persist in supplication. Beware lest Allah sees you where He has forbidden you to be, or misses you where He has commanded you to be.