Different results for between/within groups and within group regression analyses

Dear all,

from CrossValidates I was suggested to repost my question to you, as it is a technical question about R and mixed models.
Particularly, as I have a thesis to hand in in a few weeks, I hope you are able to help me understanding some problems that I cannot figure out by myself.

In this case, I have used the function lmer() to look for an interaction between groups and then used the function predict() to plot the fits for each group on a graphic.
Then I applied the lmer() to just one of those groups (same formula, technically) and used the predict() function to plot the fits for that specific group. I was thinking to obtain the same graphic for that group type and instead I obtained two different results.

I explained the process, models and presented the plots in this post:
https://stats.stackexchange.com/questions/322608/different-results-for-between-within-groups-and-within-group-regression-analyses

Can somebody help me understand this?

Best
Luca