I lost my proof of purchase.

You will have to contact the store some other way. However, you may find the receipt of limited use to you since Apple will not normally fix a phone from another country:

Effectively no warranty and a store may refuse it because of lacks of parts for a USA phone.

https://www.apple.com/legal/warranty/products/ios-warranty-document-us.html - WARRANTY SERVICE OPTIONS - "Service will be limited to the options available in the country where service is requested. Service options, parts availability and response times may vary according to country. You may be responsible for shipping and handling charges if the Apple Product cannot be serviced in the country it is in. If you seek service in a country that is not the original country of purchase, you will comply with all applicable import and export laws and regulations and be responsible for all custom duties, V.A.T. and other associated taxes and charges."

http://www.apple.com/legal/warranty/products/ios-warranty-document-us.html - "IMPORTANT RESTRICTION FOR iPHONE, iPAD AND APPLE TV SERVICE. Apple may restrict warranty service for iPhone, iPad and Apple TV to the country where Apple or its Authorized Distributors originally sold the device." <-- Read this as they almost certainly will refuse to do warranty coverage except where you bought it.

And were, EXACTLY, did you buy the phone? If they are not responding to your email, you will probably have to call them. They are most likely not going to send a copy of the sales receipt to someone who simply randomly emailed them asking for one...

Why do you need the receipt? The warranty generally doesn't require one and you most likely can't get it serviced outside of the US anyway.

I bought my phone in Las Vegas NV. I live in Argentina where agreements with Apple are quite new.

I sent the mail this morning so I suppose they have just read it. I trust they will give an answer.

Is my first time I need a repair and I didn't know if the sale receipt was required. Usually I my country a receipt is required in the warranty period.

Your answer is a good reference. I will try. Thanks

Visit the store and ask for an invoice copy.

I live in a different country from the one I bought my phone.

Then call the store where you bought it and see if they can help you.

I already sent an e-mail asking for a copy.

An email to where?

To the store where I bought the phone

In my chat with the Apple Support they told me that he opened a case to ensure that a warranty repair should be developed also in my country.