Currently, if you are in a given identity (like Home) and create a new record in a private folder, that record will be created as part of that identity. Thus when the record is created it will show in the list of records as expected.
If you then edit that record and move it to a shared folder and save the record, the record will lose the assigned identity and will no longer appear to be in your list of records. In order to see the record you must switch to the All identity. (And to see it again in your other identity like Home you must add the record to that identity.)
This is bad because the behavior appears to a user to be that moving a record from a private to a shared folder deletes the record! That is because after you move the record to a shared folder the record appears to disappear due to no longer being part of the identity you are currently using. (And even worse, a non-shared copy of the record appears in the Deleted records since technically moving a record from a private folder to a shared folder deletes the private record and makes a new one in the shared folder.)
The only way to avoid this is to switch to the All identity before you move any record from a private folder to a shared folder, then after moving the record assign any desired identity to the record.
LastPass support insists that this is correct and expected behavior and that only a new feature request with enough support can get it fixed/changed.
Please add your support. (Note that this has been tested on a Teams account, if anyone can confirm this on other types of accounts that will help technical support and the developers when they implement this fix/suggested new feature.)