For part of my support career, the team and the customers were rarely awake at the same time. Tickets came in while we slept and got answered while they did. When that is the shape of your day, the quality of your handoffs matters more than the speed of any single reply.
Write for someone with zero context
The teammate picking up a ticket after you may have never seen it. So I stopped writing notes to myself and started writing them to a stranger: what the customer wants, what I already tried, what is blocked, and what the next person should do. If my note needs me there to explain it, it has failed.
Status is a promise, so keep it honest
Tag every open ticket with a real state — waiting on customer, waiting on engineering, ready to close — and update it the moment it changes. A queue full of accurate statuses lets the next shift triage in minutes instead of re-reading everything from scratch.
The end-of-shift note
Before logging off, I leave one short summary for the next person: anything urgent, anything promised to a customer with a deadline, anything likely to blow up. It takes five minutes and saves the next shift an hour of guessing.
Decide what can wait, and say so
Async does not mean everything is instant. Some issues genuinely need the next time zone's specialist. The trick is telling the customer clearly: "The right person for this comes online in about eight hours and will pick it up first thing — here is what I have done so far." A clear wait beats a fast non-answer.
Good async support is mostly writing. The teams that do it well are not faster typists; they are clearer ones.