Use iCloud Messages with a web browser if available through Apple services
Open Chrome on your Chromebook
Go to iCloud.com
Sign in with your Apple ID
Check whether Messages is available in your account
Use a remote access app to view your iPhone screen from the Chromebook
Install a remote desktop app on the iPhone and Chromebook
Sign in on both devices
Open Messages on the iPhone and mirror the screen on the Chromebook
Use a third-party texting service if your messages are synced there
Check whether your carrier offers web messaging
Use an Android phone with Messages for web if you also need cross-device texting
Keep your iPhone connected to Wi-Fi and signed in to iCloud for syncing
Enable Text Message Forwarding on the iPhone if you have another Apple device
Use a Mac as a bridge if you have one available
Access Messages on the Mac and view it remotely from the Chromebook
Use email or cloud notes to save important message content manually