Another parent says they can pick up your child on Thursday. They're going to the school for their own child, and they walk the same way home. Before you count on that Thursday, agree on what happens from the school door until your child is back with you.
Agree on the day
Start with the date and dismissal time. Is this one Thursday, every Thursday, or a day you can ask about when needed? If pickup will repeat, agree on how much notice either of you needs when a week changes.
Make sure the other parent will actually be there when school lets out. Someone who collects their child from aftercare at 5:30 cannot pick up yours at 2:45. Knowing the parent is one part of it; their schedule has to fit the day.
Tell the school and your child
Ask the school what it needs before another adult can collect your child. Follow its current instructions, complete the authorization ahead of time, and check which name the school will see.
Your child needs to know who is coming and where to wait. The other parent needs to know the door or dismissal line, plus what to do if they cannot find your child. Sort that out before children start coming out of the building.
Decide where they will go
"She can come with us" could mean a walk to the other family's home, a stop at the playground, or a trip to your building. Agree on where you will meet them and when you will take over.
The first plan can be small. Both children might walk to one building, with you meeting them at the front door at an agreed time. Choose what both families are comfortable with, including whether the plan covers a snack, an activity, or more time together. The other parent should not have to guess.
Make it easy to reach each other
Exchange the numbers you will answer that afternoon. Decide whether the other parent will message you once the children are together. Agree on whom to call if a train or meeting makes you late.
Give the other parent the information they need for this pickup. If the handoff changes, they should have your number without searching an old class thread or calling the school office.
Decide what happens if someone cannot make it
If the other parent is sick, delayed, or cannot get to school, who will collect your child? If you are late to the handoff, how long can they stay, and whom will you call next? Agree on those limits before the first pickup.
Depending on your situation, another adult in your household, a family member, or paid care might be available. Tell that person what you have in mind and get their agreement. A name in your phone is not a fallback until the person has said yes and the school has any authorization it requires.
Once you have agreed on the details, send a short recap: "Thursday the 24th, you'll pick up both kids at the main door at 2:45 and walk to your building. I'll meet you there by 3:30. If either of us is running late, we'll call." Use the actual date, door, and time you agreed on.
That covers one Thursday. You can talk later about doing it again. If you are still working out who could take a day, start with the backup childcare options for that afternoon.