This is happening because same user has different user Id in different site (collections).

The user ID & information is stored in hidden User Information List at site collection level.

This is happening because same user has different user Id in different site (collections).

The user Id & information is stored in hidden User Information List at site collection level.

You can read more about user information list at: User Information List in SharePoint All details

So here is what you can try:

Before saving people picker data in list in different site collection, ensure that user is already added in new site collection & get user Id from that site collection.

Then set person or group column using the ID you get from different site collection.