Hi there LD72,
We're certainly sorry to hear about your mother and we offer our condolences.
While you can't directly save or transfer iMessages to an external hard drive, you could take screenshots of the messages and then export those photos to a Mac or PC to then save on an external drive. Learn how here: Transfer photos and videos from your iPhone, iPad, or iPod touch to your Mac or PC - Apple Support
Regarding any audio messages you've received in Messages on your iPhone, you can save them with these steps:
Share, save, print, copy, or delete a message or attachment
In a conversation, do any of the following with attachments:
- Share, save, or print an attachment: Tap the attachment, then tap
.
- Copy an attachment: Touch and hold the attachment, then tap Copy.
- Share items from another app: In the other app, tap Share or
, then tap Messages.
- Forward a message or attachment: Touch and hold a message or attachment, tap More, select additional items if desired, then tap
.
- Delete an attachment: Touch and hold a message or attachment, tap More, select additional items if desired, then tap
.
You'll find more information in this link: Send and receive photos, videos, and audio messages on iPhone
We hope this information is helpful. Let us know if you have any more questions.
Take care.