Since I just transferred a group with some Yahoo! induced hiccups, I thought I would write down the steps as they make sense to me. Perhaps this will be helpful others.
1. Start the first transfer request.
2. Note what Yahoo! didn't provide groups.io with to transfer, such as files or photos or databases or whatever. If nothing, stop.
3. Go to https://groups.io/yahootransfer and in the lower right corner, it says "In Process".
4. Select the appropriate group from the drop down to the right of "In Process".
5. Delete the current request if required.
6. Fill out the form requesting a new transfer and only check the boxes for what was missing in 2.
7. Wait for the transfer to complete.
8. Go to 2.
In other words, keep deleting the current request and re-requesting until you get everything you need.
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