are we allowed to just make dua during the last third of the night and not pray. in the UK waking up for the last third is becoming difficult as we get closer to summer. will just making dua include me in the hadith about Allah accepting the supplication and tawbah of His slaves .

Ustadh AbdulAziz al-Haqqan

Yes, it is permissible and you are correct. You are included in the Hadith when Allah (Subhanahu wa ta'ala) descends and asks: "Who asks Me, and I grant him? Who seeks forgiveness, and I forgive him?" (until the end of the Hadith).