What are you using to do the "sync"? What does the documentation for that say?
Also, "Resolved reason" is a custom field, possibly plain text, whereas "Resolution" is a system drop-down field. It may be that the fields are incompatible
We recently released a plug-in that synchronized for JIRA. You can select which system or custom fields will be transferred from the remote issue. I think Sync for JIRA plug-in will solve your problem:
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