There are some cases when Homeroom are not showing in Edsby for Teacher or HomeroomID and RoomID is not syncing.
1). Please make sure Room Number in SIS is of only 4 Character or less as Webservice API is not able to process if the Room Number is more than 5 character.
2). In Some cases, Designation value have extra spaces in Homeroom and only way to remove them enter some new value and save the Homeroom and then Edit the Homeroom again and Enter the Original Value back.
Once above information is corrected it will fix the Homeroom sync with Edsby or other Vendor also and changes will reflect in next sync.
Above Issue will fix the Homeroom sync with Edsby or other Vendor also.