A shift report is only useful if the population it counts is the population you think it counts. Most disputes about a till are really disputes about what was included.
Payments are attributed to the session that took them. Cash movements — pay-outs, float adjustments, hand-over corrections, debt collections — flow through the same in and out totals, so the expected-cash figure is derived from the ledger rather than typed.
Only cash moves a drawer. A bank transfer collecting a receivable writes no cash movement, because inventing one would make the cashier short on their count for money that never passed through their hands.
A drawer closed with a mis-keyed float or a wrong count can be amended afterwards by an owner, with a mandatory reason, and every derived total is recomputed from the ledger rather than hand-typed — but the amendment is visibly an amendment, forever.