May versus would
Both of them are grammatically correct but the first one is semantically wrong. So you can use the second one but I'd prefer:
Could you send me a screenshot of the application you are developing?
Even politer:
Would you mind sending me a screenshot of the application you are developing?
I would say
Would you send me a screenshot of the application you are developing?
or like Mehper said
Would you mind sending me a screenshot of the application you are developing?
Because "May you..." sounds funny and I think "Could you..." asks if they have the ability to.