how many days will take it to approve the claim for lost phone

Assuming you filed a claim to Apple by using this support page:--> File an iPhone Theft and Loss Claim - Official Apple Support, contact Apple Support about that, using this link:--> Get Support .

If you mean something different, please better specify your needs.

Regards

Giulio

The link that Giulio provided also gives you a link for checking the status of your claim. No where in the documentation does it indicate how long it can take, and my guess is that it is calculated in business days, so the weekend would not count. Use the link and see what you can find out about the status of your claim.