Hello all, i’m very very happy with my Eos fairphone 4 but i am passing it on to my daughter and she wants google. so can i reinstall my fairphone 4 with the original os from fairphone? if so how. many many thanks.
Regain your privacy! Adopt /e/OS the deGoogled mobile OS and online services
Fairphone Official Documentation : revert to Fairphone OS from an alternative operating system
You can, as @piero says. An alternative would be to install LineageOS and GApps, as described in the LineageOS FP4 Wiki pages
I would say it is about time for a good talk with your daughter. 
Well, I think most of us here in the /e/OS community would concur. However, I think that it isn’t quite that simple.
(please forgive the topic hijack)
I know not from where Ogduin hails, but in the US, Google has largely taken over the education market from Microsoft. As a result, lots of students are required to use their school-issued Google account do to their work. This also bleeds into non-work-related tasks, like paid games, messaging apps, RCS, and other areas where the /e/OS Google-free stance that we see as features will readily look like bugs to those used to Google’s seamless integration. Even consider things like Google Play gift cards; it’s messy-at-best to use them with App Lounge.
We in the /e/ crowd have our reasons for going out of our way to use something different than everyone else, but individuals of that age are likely more concerned with peer acceptance than privacy. That’s a whole other rabbit hole I’m not going down, but the odds are good that the advantages of /e/OS are minimal for someone in that demographic, when compared to the disadvantages. Not being able to do my schoolwork and being hamstrung in communicating with my friends would outweigh the advantages of /e/OS, which are difficult to quantify at that age. It’s completely understandable why a degoogled OS would be unappealing.
(back on topic)
While I personally prefer when phones have the option of Googled and deGoogled ROMs available for them, it looks like the options for this phone are either the first party FairphoneOS, as linked by Piero (the screenshots on the fairphone website show the Google apps), the Lineage + GApps noted by Petefoth…or a different phone. Not a lot over at XDA that isn’t degoogled, and none of the major ROMs I looked at had Fairphone builds, either.
My personal take: revert to stock. I can’t speak from personal experience, but I get the vibe that Fairphone doesn’t put any barriers in place that prevent flashing the Googled version of the first party release, even if you bought the variant that shipped with /e/OS. I don’t think you’re going to have a better option than that.