Icloud

You can achieve this if you restore the backup of your lost iPhone to the new iPhone.

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

This presumes you did a backup though, which you did not indicate.

Pennieterry Said:

"Icloud: How do you transfer all info from a lost phone to a new iphone"

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Backing Up Items:

Sync Through iCloud:

Note that all downloads would be lost. So, make a note of Apps that were downloaded. Also, enable items in iCloud, so that all is backed up. As an example, here is how to backup Contacts...

I. Enable Contacts in iCloud Settings:

Is Contacts enabled in iCloud Settings? If not, then enable it, and see if it pops up. If so, then it is gone amongst all devices associated to your Apple ID. So, to enable it:

A. Enabling on an iPad:

Enable Contacts in iCloud:

1. Go to: Settings
2. Tap: your name (top item)
3. Tap: iCloud
4. Tap: Contacts (so that it is green)

and...

B. Enable on a Mac:

Is Contacts enabled in Apple ID on your Mac? If not, enable it.

1. Go to: System Preferences
2. Click: Apple ID
3. Enable: Contacts