I very much appreciate you help but I don't think you completely right regarding my case.
1)
We have to file tax as green card holders. Maybe IRS doesn't have any special rules about it but USCIS has! When you renew your green cards, or apply for citizenship, you will be asked to supply copies of the tax returns you have filed. If you don't file tax, your application can be refused and you could be forced to leave the US. I now such cases. You need to show to USCIS that you have immigration intentions and a tax refund is a very good bet for it. Even an immigration officer at the port of entry could ask it if you were aboard more then half of a year.
2)
It doesn't matter when we've received a green card. DV visas, when stamped by the immigration officer at the port of your arrival (the airport where you went through the immigration) become your official green card. That is why they're stamped as I-551 - they are I-551 (the official document certifying to your status of a permanent resident alien)! Stamped visa is as good as the physical green card for 1 year, during which you're expected to receive your physical card, which is what indeed happened in my case.
3)
Dear Taxing Matters, you said that I can file a tax form from the moment as I have become a permanent resident but not from the whole year. In my case, it was September 2019. Could you please share any publication or article from IRS where it is said that it is possible? I've read Publication 519, Publication 54, Publication 514 and I didn't find such information. In my understanding, it is not technically possible to file tax for part of a year unless you file dual status.
Thanks,
Alex