When using emojis on phone, some of them are not visible properly when opening the site on PC.
Can I change that somehow?
That is how it is showed on PC:
The appearance of emojis can vary depending on the device and operating system being used. There is no way to control how emojis will appear on different devices or platforms, but using commonly recognized emojis may increase the likelihood of consistent display. PeopleNet Fleet Manager
All you can try is updating your devices in order to use the latest font files.
Even then the result may be not 100% perfect and some emojis may still look different, appear black/white or are missing completely. See