Lost Green Card and Name Change

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My father has an Indian passport and a green card, he recently traveled to Mumbai and lost his green card there. Also, he recently updated his name on the passport and would like to get his name on the green card corrected accordingly. He plans to travel back to the US around late April. What should steps he should take?
My thoughts:

1. As he get closer to travel date (~30 days) he should submit I-131A at the US Consulate in Mumbai to get a Boarding Foil to travel.
2. After he reaches the US, file I-90 for name change on the green card.

Does that seem right? Any alternate paths?
Is there a way he can get a new green card with the updated name in one-step, while in Mumbai?
Thank you.