I think everyone has explained the how and why, but not any real solutions that don't involve using a completely different application. I don't have an iPhone in front of me, but with Android you can share as a link to Google Photos instead of sending the picture/video directly. I am pretty sure you can do something similar with iCloud. Have her try the share as iCloud link instead.

Update: I just tested it. I had them open up Photos, go to the image/video, tap the share button, and then if you scroll down a tiny bit there is a share as iCloud link. I was able to view it just fine on my Android phone.

Messaging between iPhones uses iMessage and messaging between android probably uses RCS, both of which do not have the limitations of MMS, which is a limit of around 3.5 MB for most carriers. “Texting” pictures and videos from iPhone to android or vice versa will likely use MMS, hence the blurry media. Until Apple joins the party, the solution is to use another app like WhatsApp, telegram, signal, etc.

Apple intentionally makes iPhone-Android interoperability crap in order to sell iPhones. That's not conspiracy theorizing, Tim Apple blatantly admitted to it.

https://www.theverge.com/2022/9/7/23342243/tim-cook-apple-rcs-imessage-android-iphone-compatibility

Keep a stock message on your phone to cut and paste whenever an iPhone user sends you a potato-quality video. This is mine:

Please don't send video to me via iMessage from your iPhone. In fact, you really shouldn't send video via iMessage at all. Video sent by Apple looks terrible on non-iOS phones. This is not a shortcoming of other phones, this is entirely Apple's fault and is their explicit intention. If you want to send a video from your iPhone, you can open the Photos app, tap the share button, and select "share as an iCloud link". That will enable All users to view your glorious video of your cat/kids/dinner/vacation/rant/whatever in the high resolution that your overpriced phone is capable of. Another option is to send the video using a messaging app such as Signal or WhatsApp. Alternate messaging apps are what most of the world use in lieu of sms/mms text messaging.

This is a form letter response and you will get it every time you send me video from your iPhone via iMessage.

P.S. I love you

Use Whatsapp or another 3rd party messenger. It's annoying but an easy solution.

What do the videos look like on her phone?

If they're shit there, it's the phone (or the operator). If they look good there and change to shit when they get to your phone, it's something in that process. Perhaps set to send a low res version by default.

You're probably getting suggestions for what she should do different because, at least at a starting point, it could just as easily be something her phone is doing before sending as it is something your phone is doing on the receiving end.

I've had a phone say 'video to big, do you want to crop or share through abc app' before. Don't recall the exact message, but seems more likely than you phone downgrading something it's receiving.