The Suggestion spell influences a creature by suggesting a course of action:
You suggest a course of activity (limited to a sentence or two) and magically influence a creature you can see within range that can hear and understand you. Creatures that can’t be charmed are immune to this effect. The suggestion must be worded in such a manner as to make the course of action sound reasonable. Asking the creature to stab itself, throw itself onto a spear, immolate itself, or do some other obviously harmful act ends the spell. The target must make a Wisdom saving throw. On a failed save, it pursues the course of action you described to the best of its ability. The suggested course of action can continue for the entire duration. If the suggested activity can be completed in a shorter time, the spell ends when the subject finishes what it w as asked to do. You can also specify conditions that will trigger a special activity during the duration. For example, you might suggest that a knight give her warhorse to the first beggar she meets. If the condition isn’t met before the spell expires, the activity isn’t performed. If you or any of your companions damage the target, the spell ends.
The description suggests the idea that this course of action sounds reasonable to the target, in such a way that it could be a decision that the target took on his own. Furthermore, contrary to other illusion spells (e.g. Friends), the target won't notice that he has been charmed.
However, I am not sure whether the ideas suggested by the spell persist after the spell ends. Consider the following example:
A creature owns a magical item connected to evil forces. He is using that item for his purposes. Another creature casts Suggestion by saying: You feel that this item is ruining your soul. You will get rid of it, and you will go praying for 2 hours in order to purify your soul.
Supposing that the target considers it reasonable, he gets rid of the item. Then, for some reason, the spell ends. Now, How will the target react? Will he keep considering that idea reasonable, or will he try to get the item back?
This leads to the title question: do the ideas that justify the Suggestion spell persist after the end of the spell?