Transfer Value of Field to Another Field under Content Type Manage Fields
No, this is not easily possible through the Drupal interface. You will need to execute a custom SQL query to move your data from one field to another.

The following two queries will copy all field data from field_image to field_screenshot for each entity where field_screenshot is empty.

INSERT INTO field_data_field_screenshot
SELECT a.* 
FROM field_data_field_image a
LEFT JOIN field_data_field_screenshot b ON a.entity_id = b.entity_id
AND a.entity_type = b.entity_type
WHERE b.entity_id IS NULL


and

INSERT INTO field_revision_field_screenshot
SELECT a.* 
FROM field_revision_field_image a
LEFT JOIN field_revision_field_screenshot b ON a.entity_id = b.entity_id
AND a.entity_type = b.entity_type
WHERE b.entity_id IS NULL


After running this you can then delete the first field. 

If field_screenshot alreadly has data that you want to overwrite you will need to  delete it first using these queries. Make sure this is what you want to do first because this WILL delete your data

TRUNCATE TABLE field_data_field_screenshot
TRUNCATE TABLE field_revision_field_screenshot