Question about the ending (spoiler)

So.... they have this big argument in the kitchen, and Luis tells Fran about how his mother walked out etc. Then they are driving through the rain, they stop at a house, Luis asks ran if he wants to meet 'her' - Fran says no. Luis gets out and goes to the door with a piece of paper, comes back to the car and they drive off. Fran asks if it was his mother. Luis doesn't answer, but after a few minutes he gets out and starts to cry, and Fran gets out too and hugs him.

I suppose my question is the same as Fran's. Was that his mother? And what happened? What was the piece of paper?

It was a good film. I enjoyed it. I just wonder what others think of the ending.

PS Yes I know there was an additional scene after the credits (the one at the beach).
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"Maybe I should go alone"
- Quint, Jaws.