"We have introduced him to our boss."
Translation:Przedstawiliśmy go naszemu szefowi.
If the group is "oni" - "przedstawiliśmy" If a group is "one"- przedstawiłyśmy
Oni= masculine personal gender-
the most common groups:
oni-masculine personal gender
- group that includes one male person
one not masculine personal gender ("other" in wiktionary tables)
- a group of female people
- a group that does not include a person,
"Oni" and "one" means "they", so I'm not sure that you can be in such group if you're the person talking ;)
What you were talking about here is the distinction in the 1st person plural. When you are included in the group ("we" = "my") or when you're using 2nd person plural ("you" = "wy") the verb form changes depending on the gender (like here przedstawiliśmy/przedstawiłyśmy for 1st person plural), but the pronoun has only one form. The pronoun has different forms only in 3rd person plural, and of course the verb changes as well.
My byliśmy (we were, either all male or a mixed group), but My byłyśmy (we were, all female)
Wy byliście (plural you were, either all male or a mixed group), but Wy byłyście (plural you were, all female)
Oni byli (they were, either all male or a mixed group, but One były (they were, all female)
The gender is visible in the verb form in past tense and future compound, but not in present or future simple.
Maybe this comment was not needed, but I felt that you may have gotten something wrong here so I decided that it's better safe than sorry.
There are no other "They" than "Oni" and "One" - well, not in pronouns. Usually you will just specify the group: "Moi przyjaciele", "Tamte kobiety", etc.
What I imagine immery meant is that sometimes there are other possibilities to incorporate under "oni" and "one", but they are generally not very important. But for example a group of personified animals, if at least one of them is male, will be "oni": Kaczor Donald i jego dziewczyna Daisy zjedli obiad w restauracji.