Einsam using Himmel instead of her teacher to lure in Frieren shows how important Himmel was to Frieren and how well she remembers him.
Einsam in the anime Frieren: Beyond Journey's End (Sōsō no Furīren) is a creature that lures people in by showing them their loved ones, typically ones that are already dead. A lot of people cannot resist the vision and fall prey to Einsam.
We will spoil Frieren's and Fern's encounter with Einsam here. Go take a look at the fifth episode before coming back; it is worth a watch!
As Frieren and Fern travel through the woods, Fern sees Heiter, her old teacher, the man who saved her life, and she cannot help but fall for the lure. Fortunately, at the same time, Frieren sees Himmel, and she easily destroys the illusion with a magic blast, leaving Einsam visible to Fern, who finishes it.
One might notice that both sorcerers give rather excessive blasts of power when fighting Einsam, which might or might not indicate that they were angry with the creature.
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For Frieren, though, it is also important that her previous meetings with Einsam involved her old teacher, who would be crying for her not to hurt her. Now, it is Himmel, and he tells her to shoot, which, according to Frieren, is absolutely what a real Himmel would say.
Frieren starts the new journey partly because the death of Himmel changed her a lot. She remembers never trying to learn about him, and she genuinely believes that he had wasted the time they were together since she never tried to be a real friend.
Einsam selecting Himmel as lure for Frieren does show how much Frieren cares about him and how much he matters to her. At this point, even Frieren's teacher cannot compete.
But moreover, Einsam creates a very realistic depiction of Himmel, which, presumably, it takes from Frieren's memories. Frieren is mostly changed by the fact that she did not learn enough about her mortal friends, but when Einsam shows her the version of Himmel she remembers, Frieren seems to find it quite authentic and similar to the real thing. In other words, her memories are not lacking, and Frieren was not that disinterested and passive in her relationships with her travel companions since she remembers them so well.
Einsam does not just show that Frieren dearly misses her friends; it also shows that she remembers them well enough for a realistic copy to be made from those memories. Frieren is shown to be a very good friend in this episode.