If using Outlook, query the GAL directly, or download the latest OAB. Before you do anything send the user you created a 'Test Email' from your own account.
Also in the properties of the mailbox database, your users are using, make sure it points to the correct public folder database.
This situation however is extremely rare since the default maintenance time on Exchange is at AM and updates and downloads are usually performed during working hours.
Even though Outlook is the last in the chain, it is often the first level where the troubleshooting takes place as usually this is where the request is coming from.
In this guide, the relevant timings are explained and instructions are given in how you can directly force an update and resync, which can be very handy when troubleshooting or when you work in an Exchange environment which sees a lot of user mailbox mutations.
This means that in the worst possible scenario, an update to the Address Book won’t become available to the user until 48 hours after the change.In that case the whole OAB is being downloaded again.