Reading both Summoner's Charm and Shadow Conjuration, I feel that it should not interact with each other.
Summoner's Charm (Su) states that:
Whenever you cast a conjuration (summoning) spell, increase the duration by a number of rounds equal to 1/2 your wizard level (minimum 1). This increase is not doubled by Extend Spell. At 20th level, you can change the duration of all summon monster spells to permanent. You can have no more than one summon monster spell made permanent in this way at one time. If you designate another summon monster spell as permanent, the previous spell immediately ends.
Shadow Conjuration is an Illusion (shadow) spell which states that:
You use material from the Plane of Shadow to shape quasi-real illusions of one or more creatures, objects, or forces. Shadow conjuration can mimic any sorcerer or wizard conjuration (summoning) or conjuration (creation) spell of 3rd level or lower
Due to the fact that Summoner's Charm only interacts with Conjuration (summoning) spells and not Illusion spells, Shadow Conjuration would not work.
However, in Greater Shadow Conjuration, it is stated that:
This spell functions like shadow conjuration, except that it duplicates any sorcerer or wizard conjuration (summoning) or conjuration (creation) spell of 6th level or lower.
Now instead of mimicking the spell, it duplicates it. The term "duplicates" confuses me in this situation. Does that mean that it is now an actually Conjuration (summoning) spell or is it still an illusion spell? Why is the term "duplicate" used instead of "mimic"? Or am I just reading it wrong?