Evaluating Two Versions of Overlapping 1010 Moore Automaton Sequence Detector: Help Needed

Hello, I am supposed to make a graph of Moore automaton sequence detector 1010 overlapping, i.e. the last symbol detected
sequence is the first symbol of the new sequence. And I've been thinking about two versions and I don't know which one is good. Please help me evaluate. I think the lower version is correct. I don't know yet if q4-> z0-> q2 or q4-> z0-> q0, but I think the latter option is fine for the non-overlapping version. Additionally, in this command, I do not understand the logic that the last symbol, which is 0, is to be the beginning of a new sequence that starts with 1, so do I not understand something, is the task poorly constructed?

https://pl.wikipedia.org/wiki/Automat_Moore%E2%80%99a
http://www.zsk.ict.pwr.wroc.pl/zsk/repository/dydaktyka/tech_cyfr_inz/tc1inz_05.pdf
http://www.cs.put.poznan.pl/rwalkowiak/pliki/ptc/ptc_w4.pdf

So for sure the lower graph is good, but I still don't know what in the last state of q4, because in the "overlapping" version the last symbol, which is 0, is supposed to be the beginning of a new sequence that starts with 1, so if I don't understand something, or the task is poorly structured?

This is a homework assignment so you have to solve it yourself.
We can only identify mistakes and help correct them.

After all, I solved myself, I am just asking about the sense of this problem, this is the beginner electronics section, how do I know if there is a catch here, in my opinion, as I wrote earlier, the overlapping version of this sequence does not make sense and I ask for opinions if it is good I think.