Transcription, like document analysis, is not always an exact science and there's a certain amount of "creative" element to it. One must be careful how one interprets the use of "creative" in this sense. Creative in this case is thinking outside the box, not in the sense of making things up. The ability to judiciously use the "creative" element cf transcription comes from practice and from reading document after document.
Who Wrote this Document?
I'm not certain, but the signature of Julius Jenkins is similar to the handwriting of the document, making it appear he was the actual writer.
Jenkins was the maiden name of Lake's wife and is a probable relative. However, that's not even vaguely indicated by this document (there's no law that relatives have to write things). The fact that Jenkins probably made out the document only indicates that he was trusted to make it out correctly. He may have been one of the "nearby" kin who was familiar enough with how such letters should be written and so he "got the job." He could just as easily have been more closely related to Beesly than to the Lakes or not "related" to anyone else on the document at all.
And it goes without saying that all these individuals were associates of one another in some way.