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"Save checklist data to Jira custom fields" option must be enabled in Issue Checklist Global Settings. 

Guide

1. Go to Automation listing page (it is either Project settings > Automation or Jira Settings > System > Automation rules) and press Create rule button:
   
   
   
   
2. On the New trigger page, Select Field value changed option:
   
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3. On the Field value changed page select Checklist Text in the first list and then select Edit issue in the second list. Next, press Save button:
   
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4. On the Add component page select New condition option:
   
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5. One the New condition page select if / else block option:
   
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6. On the If block page press Add conditions... link and next select Advanced compare condition:
   
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7. On the next If block page enter following details in the form:
   
   1. {{issue.customfield_10268}}
   2. contains regular expression
   3. (?m)^\*\s+\[(x|done|skipped)\]\s+Test
   
   Where:
   (1) customfield_10268 is an ID of Checklist Text custom field that you must replace with value from your Jira. Read how to find custom field ID.
   (2) Test is a text/summary of checklist item that we want to test for checked status (replace it with summary of your checklist item).
   
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   Press Save when finished.
   
   
8. On the New component page select New action option:
   
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9. On the New action page select Edit issue option:
   
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10. On the Edit issue page select Label field from the dropdown, change form option to Add/remove values and provide a label that you want to add to an issue:
    
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    Press Save when ready.
    
    
11. On the Add component page select Add else option:
    
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12. On the Else block page press Add conditions... link and next select Advanced compare condition:
    
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13. On the next Else block page enter following details in the form:
    
    1. {{issue.customfield_10268}}
    2. contains regular expression
    3. (?m)^\*\s+\[(?!x|done|skipped).*\]\s+Test
    
    Where:
    (1) customfield_10268 is an ID of Checklist Text custom field. Read how to find custom field ID.
    (2) Test is a text/summary of checklist item that we want to test for unchecked status.
    
    Please note that the regular expression from point (c) differs from the one in (7c)
    
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    Press Save when finished.
    
    
14. On the New component page select New action option:
    
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15. On the New action page select Edit issue option:
    
    
    
    
16. On the Edit issue page select Label field from the dropdown, change form option to Add/remove values and provide a label that you want to remove from an issue:
    
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    Press Save when ready.
    
    
17. The rule configuration is complete. Provide a name for the rule and press Turn it on button:
    
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18. Test the setup and enjoy 
    
    
    1. Go to any issue page, add "Test" item and:
       
       1. check the Test item to notice label "Test_checked" added to issue
       2. uncheck the Test item to notice label "Test_checked" removed from the issue
       3. check/uncheck other items to notice that label "Text_checked" is not affected
    
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