The message "More results will be shown when messages finish indexing" on an iPhone usually appears when the Messages app is still processing and indexing the data to make it searchable. This can happen after an iOS update, restoring from backup, or if there are a lot of messages and attachments to process. The indexing process typically takes a few hours but could take up to 24 hours or longer depending on factors like the number of messages, their size, network speed, device performance, and available storage. To speed up the completion of message indexing and resolve this issue, here are effective solutions:

• Restart the iPhone to refresh the system.
• Toggle iCloud Messages off and on in Settings.
• Adjust search index settings by toggling search options for Messages in Settings under Siri & Search.
• Ensure the device is connected to a fast, stable Wi-Fi network and plugged in to charge.
• Update the iOS to the latest version.
• Temporarily turn off iCloud backup to download the data locally.
• Reduce the number of stored messages or delete some older messages to lessen the indexing workload.

Following these steps can help complete the indexing process faster and restore full message search functionality on the iPhone.