Couldn't restore iPhone after received new one with same capacity

Hello,

If you really have that much data, you should have a phone with more storage space. Otherwise, you'll constantly run into storage issues in the future.

You said that you just got the new phone. Where did you get it? Can you still return it? Then get one with more storage.

Otherwise, consider restoring your data from iCloud using one of the other methods. See this:

Transfer content from your previous iOS device to your new iPhone, iPad, or iPod touch

Good luck.

Ensuring a comprehensive backup of your iPhone 13 Pro MAX through iCloud might necessitate exceeding the allocated 50GB storage from your subscription. The extent of storage required hinges on the amount of data currently occupying your iPhone. In essence, the adequacy of your iCloud storage is contingent upon the total data size on your device.

In other words, the 50GB iCloud Storage plan may prove insufficient if your iPhone 13 Pro harbors a substantial volume of data. Factors such as photos, videos, apps, and other content contribute to the overall storage requirements for an effective backup. Thus, it becomes imperative to assess your current data utilization on the device to gauge whether additional iCloud storage might be warranted for a seamless and comprehensive backup experience.

Do not forget to tap "Show all Apps" to see all the apps' data that is getting backed up.

Watch the GIF below to know the size of the next backup.

Your iPhone may have much more than 50GB of iCloud Storage that you have.

Check how much space is required for the backup.

Watch the iTunes/Finder BackUp Size on a GIF below

Note: Backups are compressed. (During restoration it will expand)

See the GIF which shows 28.03 GB used space on iPhone 6 and the Backup Size is 5.26GB. So it can never be larger than iPhone used space/storage.

Same is true for iCloud Backup too. What you see the size is compressed Size

iCloud backup size on iCloud is 3.5 GB for the same iPhone same date that is because iCloud backup doesn’t include information that are synced and stored in iCloud, like Contacts, Calendars, Bookmarks, Mail, Notes, Voice Memos, shared photos, iCloud Photos*, Health data, call history, and files you store in iCloud Drive.

*-If you had turned on iCloud Photos, your content is automatically stored in iCloud. 

Watch the GIF below

Do not crop the screenshot.

To improve my understanding of the phenomenon, it would be highly beneficial if you could share a full screenshot (Do not crop it). Visual representations carry a greater impact than written descriptions.

Please remember that this is a public forum, so when attaching a screenshot, please avoid including any personal credentials such as IP addresses, card details, email IDs, Apple IDs, IMEI numbers, serial numbers, phone numbers, order IDs, or any identifiable location information if you are sharing a map.

With the limited information that you have provided, It is hard to even guess the problems faced by you. 

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Please re-post with detail so that someone else can help.

If the backup size is 251 GB and your new iPhone has 239 ?