The most (if not the only) sensible way of mapping Remaining Estimate to the MS Project *Work fields is either
Remaining Estimate + Time Spent => Work or
Remaining Estimate <= Work - Time Spent,
depending on the desired direction of synchronisation. This is the default configuration in Ceptah Bridge.
Always consider how fields are related in MS Project. For example, mapping both Work and Finish with the direction from JIRA to MS Project will not work properly because changing Work will change Finish and updating Finish resets Work. It is extremely unlikely that both mappings will produce compatible results, thus one of the fields will always be out of sync. The solution here is to configure one of the mappings to copy data from MS project to JIRA. This is a sensible thing to do because it will allow utilising MS Project for what it is good at - planning and scheduling. It will take effort from JIRA, schedule the activity and send back the Finish date. Alternatively, you can import Due Date, calculate the effort required to arrive on it and publish the Remaining Estimate in JIRA.
It may appear logical to map Remaining Estimate to Remaining Work, but, in practice, this will not work because MS Project will automatically reflect any Remaining Work changes in the total Work field, and the task will grow or shrink even if the total effort in JIRA has not changed. For that reason, the Remaining Work field is not available in the drop-down.
Mapping Original Estimate to Duration is not a good idea either. Firstly, Original Estimate is original and is different from the actual effort. But more importantly, these fields have a different measure - the JIRA estimates are man-hours, whereas MS Project Duration is just the number of working hours between Start and Finish. It is much better to update Work based on the values from JIRA and let MS Project calculate Duration and Finish for you. Then you may want to set Due Date in JIRA to Finish from MS Project to close the loop.
A good fit for Original Estimate is Baseline Work.
Please go to JIRA -> Project Settings, select the "Time tracking" tab, tick "Time Spent", select "Daily actual work" and then tick "For each assignment". This will populate the time scale entries for your tasks with the data from JIRA work log on user by user and day by day basis.
Please note that the option is disabled if the Assignee is mapped to MS Project Resource on the first tab page. You need to map assignee to a text field or avoid mapping it at all to enable the "For each assignment" option. The reason for the limitation is that MS Project allows assigning multiple resources to the same task while JIRA does not. "For each assignment" option implies associating multiple resources with the same task. At the same time, there is no way for the user to tell Ceptah Bridge which particular resource to use as assignee. For instance, it would not make sense to use the first resource from the Resource Names list as the order is simply alphabetical.