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NEW: A free demo version of the tool is now available. The demo version can only duplicate one field, to a maximum of 3 pages.
Acrobat has a built-in command to duplicate a single field to multiple pages, but the catch is that all of the duplicated fields are exact copies of one another, so with the same name and value. If you want unique fields, you must rename them manually afterwards (or use this tool: Acrobat -- Rename Duplicate Fields to Unique Fields)
An easier way to do it is by using this script, which lets you select a field, enter the page range to which to duplicate it, and then continues to make unique copies of the fields, so no renaming is necessary!
When you press OK, unique copies of the fields "Text1" and "Text2" will be made on pages 2 to 10.
If you have any questions regarding this tool, you can contact me directly.