Hi there yosef235,
We see you're not getting video through a projector when you connect your iPhone 7 Plus. We'd like to get a few details to work out what troubleshooting steps you can try.
First, you mentioned another device works with the same projector and adapter. Which iPhone model is that, and which iOS version is it running? Knowing that will help narrow this down. Also, which iOS version is running on the iPhone 7 Plus? That model maxes out at iOS 15, so we're wondering if the two devices might be running different software.
Also, when you tested the other iPhone, was it with the same source content? Depending on the source and the apps you've tried already, you might test a few apps to see if you get the same result or not.
This link has a few good steps as well. It sounds possible that you've tried these, but we want to share them to make sure you've covered everything: About Apple Digital AV Adapters for iPhone, iPad, and iPod touch - Apple Support
"If you need help with other issues
- Disconnect and reconnect your adapter from your iPhone, iPad, or iPod touch and from your TV, monitor, or projector.
- Make sure that your VGA or HDMI cable works, since the issue could be with the cable.
- Remove any VGA or HDMI extension cables or converters. Accessories that convert a VGA or HDMI signals to different video formats (DVI, Composite, Component) aren't compatible.
- Make sure that you have the latest version of iOS."
Take care.