There are a number of ways to prevent further editing of a form after it has been filled-in, but which one you choose depends on a number of things, such as what PDF viewers it needs to work with for the person who initially fills-in the form and whether any of the subsequent recipients will ever need to extract the form data. Some possibilities:
2. Lock the form fields or document by digitally signing.
This option is really only available with Adobe Acrobat/Reader desktop versions and a limited number of non-Adobe PDF viewers. Will not work with mobile versions of Adobe Reader. Form data can be extracted. Required users obtain/create digital ID and sign. Document has to be Reader-enabled if using Adobe Reader. Locking the document is more secure than just locking the fields.
3. Flatten the form after filling.
This is supported by Acrobat and certain mobile PDF viewers, now including Adobe Reader for Android/iOS. Since there are no longer form fields, form data is only available to be extracted as regular page contents, which means it's not easy to get at. Not available with desktop versions of Reader, apart from #4 below.
4. E-sign the form after filling.
This is essentially the same thing as #3 and is possible using the built-in EchoSign functionality of Adobe Reader 10/11 desktop/mobile versions and some non-Adobe PDF viewers. Form can be saved by Acrobat/Reader as a flattened version without actually e-signing. Form data not easily extracted as with #3. Won't work with Reader-enabled forms. Won't work if form includes a button with a "submit a form" action that uses a mailto type URL, but there is a workaround to this limitation. Won't work if form is certified or has other digital signature fields.
5. Apply security after form is filled-in.
If the person filling in the form has Acrobat, they could apply security to prevent further changes. Form data can still be extracted. Can't work with Reader and most other PDF viewers.