Groups are merely a list of existing addresses; they don't exist
independently so in order to be in a group, the address needs to be in
your address book.
Exporting the group as a vCard will export all of the data for all of
the addresses and (when that other person imports them) give the
option to add duplicate cards and/or overwrite existing folks with the
same names. When she goes to import the vCard into her own address
book, the program will warn her about this. If she wants them as a
group she will need to create the group herself, perhaps using the
"last import" group created at first as the starting point.
A simpler way (if you only want to share email addresses) might be to
address an email message to the group and then copy the "to" field
from that email, sending it to her in the "body" of an email, whence
she can copy and paste or add them to her own address book.
- Rory