You manage someone nine or twelve hours away. The overlap is a thin strip at one edge of your day. The easy habit is to drop a half-thought in the channel and catch them on the next overlap. That habit turns every small ask into a two-day loop.
They wake to a note that only you can finish. You wake to a question. The work sits in between.
This is not the same problem as three peers who must decide across a spread. You already have the authority. What you owe them is a note they can act on while you are asleep.
Count the question they would have to ask
Read the draft as the person who has only this message. Every stall is a day.
Can they tell what is decided and what is theirs? Can they see the constraint that makes the obvious path wrong? Do they know whether you want a one-line answer, a plan, or just a start?
Write for a cold reader even when they know the project. Overnight, they are colder than they look in a hallway. Chronology is your memory; current state, hard limits, and the ask are their input.
Keep anything they must have to act out of a file they cannot open on a phone at seven in the morning. RelayLink packages are text. Point at the doc; do not assume they will hunt.
Date the hour, not the weekday
"By Thursday" is three different mornings. "End of day" is three different desks.
Write an instant: Thursday the 20th, 18:00 UTC. Then look at their working day, not yours. An honest deadline that lands after they have already gone is not a deadline. It is a disappointment you scheduled.
Say what you will do if they have not answered by that hour, and mean it. "If I have not heard by 18:00 UTC I will assign the rollback to Dana and you can pick up the write-up." A default they can live with is kinder than a silent wait that turns into a 7 a.m. ping.
Separate the decision from the FYI
A report who is trying to be helpful will treat every paragraph as something they must answer. If a block is only for awareness, say so in the first line of that block. If you need a choice, name the options and your recommendation.
"I need you to pick A or B for the migration window. I recommend A. The Friday note below is background — no reply needed on that part."
One message can hold both. Mixing them without a label produces a three-paragraph reply you did not ask for, sent at the end of their day, which you then have to unwind at the start of yours.
Send it as a briefing they can pick up anywhere
You do not need a shared office chat for this. If they have a RelayLink account, an accepted contact is what opens the thread. If they do not, the briefing arrives as email and a page; they can reply from the link without signing up.
You still approve what goes out. A draft your assistant assembled from yesterday's session is useful only after you have read the words they will wake up to. Nicknames you use for them stay on your side unless you choose to share one.
The overlap hour is then free for the few things writing cannot do. If you want the first draft built from the session where you already thought it through, connect your assistant.