Update App distributed via apk download directly

we are currently testing our app and we distribute it via link to download directly the apk, now we want to change the distribution method and we are using Google Play to share it via "Open Beta Testing", but when we open the store link the button to install/update shows only "open" text. We try to update version code but we are not able to update the existing app installed via direct link. it's possible update an app download via direct link from a store link?

Thanks for your time