A single order that ships in three separate boxes creates a real risk of confusion if each box doesn't clearly explain its own contents and place in the larger order.
Number each box explicitly
"Box 1 of 3," "Box 2 of 3," and so on, printed clearly on each slip, immediately tells the recipient how many boxes to expect and whether anything is still missing.
Only list what's actually in that specific box
Don't print the full order's item list on every box's slip — each one should show only its own contents, so a recipient checking one box against its own slip gets an accurate picture, not a confusing full-order list that doesn't match what's physically there.
Repeat the shared order number on every box
While item lists differ per box, the overarching order number should stay consistent across all of them, so the recipient can clearly see all the boxes belong to the same order even if they arrive at different times.
Note if boxes are expected to arrive separately
If shipping constraints mean the boxes won't necessarily arrive together, a short note ("Your order is shipping in 3 packages, which may arrive on different days") sets expectations and prevents an unnecessary "is my order missing items" support inquiry.
Keep a clear internal record matching boxes to slips
On your own side, keep track of which items went into which box — this matters if a customer reports a missing item and you need to quickly check which specific box it should have been in.