"Jerry built" has a couple of possible sources. From an 1856 use in Liverpool, "built hastily of shoddy materials," from jerry "bad, defective". Thr jerry could also be a corruption of "jury" as used in the term "jury mast", a temporary mast put up in place of one that has been broken or carried away." and the earliest citation given is from 1616, with the spelling lury mast.
It is wrong to associate "jerry built" with anything German, unless the thing was built by a post-war German refugee working for a shonky house builder.