I'm actually surprised that this is even the real question in the fandom. But it is so.
This theory became especially popular after Ehren’s statement that Armin was influenced by the previous Collosal Titan. And suddenly half (or more) of a fandom losing sight that this (and much more) was said not because it is one hundred percent true (it is not), but as a way to influence Mikasa and Armin, to further disbalancing them: this is a very exaggerated statement mixed with some truth, necessary for the effect - to add new seed to the existing doubts.
Firstly, I somehow hardly believe that Eren, as he became, would have noticed something new about Armin that his other friends had not noticed (and uncharacteristic behavior is exactly what should follow, after a personality change). Jean is now more of Armin’s best friend and he showed no signs of concern. Like Mikasa, his other best friend, who knows him the longest. Correct me if I am wrong.
I would rather believe that Eren deliberately projects (his own?) situation on Armin (his two childhood friends DID noticed a change in him, and not for the better). Among other things, it looks like an attempt to sow discord between two of them: inspire Armin fear that this may be his future, inspire fears in the reliability of Mikasa. And vice versa.
And second: In short, I don’t believe in it simply because then it means that all the shifters from the 104th (and their peers from Marley) were and remain out of control of themselves.
This is of course a very good excuse for fans of Eren, who are the "happy" owner of a bunch of different Titans. And for him this may be true (the effect of so many titans in one carrier is unknown), but this is a slightly different question.
I mean, it is canon that a touch from the royal heir to the shifter unlocks paths/memories/whatever it is. It is canon that both Eren and Armin got skin-to-skin contact with Historia when she put medals (or what it was) on their neck. And so is the canon that Ymir also had skin-to-skin contact with the same Historia. Therefore, over the years spent in the Training Corps, she probably acquired a complete package of Marcel's memories. Marcel, who from an early age was subject to aggressive indoctrination and suggestion.
And yet she did not ignite with a sudden zeal to join the shifters. In fact, Ymir tried her best to stay under the radar. Her loyalty was solely for “Krista” and herself. Someone may say that in the end she left with Reiner and Bertold precisely because of the influence of Marcel, but I am convinced that this was also her own decision. Yes, it was taken on the basis of her knowledge, but nothing more: Ymir made this decision precisely after talking with Historia, the most important person for her, well aware of the consequences for herself (regardless of whether she leaves or remains). If something guided her, it was a guilty feeling for the unconscious killing of Marcel (because she was unlucky to get to know him through his memories - and this turned the accident into a heavy burden).
And now about our trinity of shifters. We all know that they was under Zeke's command. Zeke who is also a royal heir. This means that skin-to-skin contact took place somewhere in the training process (training hand-to-hand combat, or even an elementary hand shake). Still, the three were somehow more immersed in their own problems and torment... for people struggling with strangers within themselves.
And since none of the above has fallen victim to the introduction of someone else’s consciousness into their minds, I’m sure that no personal or emotional qualities/features are transferred from the previous shifter to the new one (the new shifters don't experiencing/living through but just observing someone else's life and experiences).
Armin is no exception. He just got an expanded understanding about the traitors - he learned about their past, about what kind of people they were. And that any others who come to replace them will be the same - mere humans - just on the other side of the war. Armin is a very standard case of titan transfer. There is nothing exceptional in this. So there are no unexpected effects (as well as with other shifters).
The founder, in my opinion, is one of two exceptions. The second is the situation with Eren, the first not royal owner of a founder.
Therefore, I don’t understand why so many people are convinced that Bertholdt (who has died and is no longer influencing anything) somehow influences Armin...
Edited by admin: title was in Russian, translated to English.
It's true that people can be influenced by their titan's previous holders, but we've only really seen this with the founding titan and the vow to renounce war. It seems like this is something only the founder can do since we haven't explicitly seen it with anyone else.
I think with Armin/Bertholdt it's more of an indirect thing due to the nature of the colossal titan. It's power is basically only good for causing huge destruction and mass murder, and both Armin and Bertholdt were pressured into using this power by their military superiors. When personality wise they both wouldn't really want to do it. Armin never even uses the colossus titan in the most recent chapters (even though it would have been very useful) presumably because of the inevitable collateral damage it would cause.
They're both basically carrying around a personal nuke every second of their lives, that's sure to change your personality somewhat.