As described you are not able to find the save or share function in order to return the changes to the initial editor.
Would you mind sharing how the link was sent to you for fill and sign? Is it through Adobe Sign (A cloud-based service)? If yes, when the signer adds his or her signature in the signature field and then clicks the Click to sign button, the agreement is sent to the next signer with a link to sign, and so on. Once the agreement is signed by all the signers, everyone gets a copy of the signed agreement via email.