I convert my videos taken with the Fujifilm X-T3 with Handbrake. One thing that happens when converting videos with Handbrake (and I assume with the most free video converters) is that it does not preserve the video's original metadata. To me, one of the most important metadata is the creation date because the Photos app on my iPhone sorts the videos by date.
Here helps me a very handy iOS app called Metapho. Version 3 of Metapho added support for videos what is an awesome feature. After I transfere the converted video to the iPhone I edit the video's date with Metapho and set the original time from the original video.
In version 3 the app is also a lot more stable since a had crashes with version 2 when I edited a batch of photos.