The timing is based on their studies. They KNOW the booster works at at 21 days, because they used those intervals in the trials. That does not mean it wouldn't work if you went a bit earlier or a bit later. They just didn't PROVE it because they didn't test it. We are asked to try to stick to the proven time schedule, to be on the safe side.
There is no benefit to getting the shot on the earlier end of the interval or the later end of the interval, in terms of efficacy. Earlier, however, means she will be ahead a week in terms of approaching her full possible immunity. So my preference is always earlier.
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