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I usually reach people by sharing into groups. But the likes there have no effect on my page.
In my previous question I asked if we can get the likes there on my posts in the page. But that was not possible.
So now my question is if I can invite people who liked my page's post in the group to like my page.
Facebook changed this in September 2011. The first time that you set the audience to specific lists or people after the change, this notice pops up:
Any custom audience set to specific lists or friends after you are shown this notice will show the list of names. If it was set before you were shown the notice (even if the same setting is still being used for new posts) will just show "Custom" as before:
If you don't want it to show the list of names, one thing you can do is post to Custom, choose Friends and under Hide this from enter a friend list or certain people that you do not want to see the post. In that case it will appear to others that it was posted to Friends as shown below; they will not see the list of names that are included or excluded. However, because new friends will not be in any friend list at first, they will see any posts that were posted this way if you don't remember to quickly add them to a list.
Another way to avoid the list of names is to post to one of the automatically generated "smart lists", such as the Family, city, and school lists. Unlike the other lists, where the people do not know which lists they are on, people are placed on these lists automatically based on their own profile information so they should already know which of these lists they are on. In this case the list is shown rather than individual names:
Edit: So in summary, if you set a post to be visible only to Friends, Friends of Friends, Public, or one of the predefined Smart Lists like Family, city, or school, it will show that (no individual names); even if you hide it from some of those people no names will be visible. If you make it visible only to Close Friends, Acquaintances, one of your own custom lists that you created, or to individual names, then it will be expanded to show the people's names (none of those list names are shown); if you hide from some people then the people you hid it from will not be in the list of names.
I don't have a definitive answer on combinations of multiple lists; it seems that there is some way to get it to say "Custom" with some but not all combinations. However even if you figure out how it currently handles multiple lists I would not count on it staying the way it is for long. Facebook is known for making frequent changes to documented behavior, but that is nothing compared to the frequent changes they make to undocumented behavior.
If you set the audience to one of the friend lists that you created, or to Close Friends or Acquaintances, the people on that list will be able to see the names of the people that can see the post (but not the name of the list). If you set the audience to one of the "smart lists" that Facebook creates automatically based on family/city/school/work, those people will be able to see the list name and not the individual names. Facebook does this to help people decide whether they want to like or comment on the post, since those same people will be able to see their like or comment.
Additional information can be found in this answer.
Best Answer
If they all are in your friend list on Facebook then yes, you can invite them to like your page.
If they are not in your friend list but you have their email id then yes, you can sent an invitation to them to like your page**.
If they are not in your friend list and you don't have their email id, there is not officially direct way to invite them to like your page.
What you can do is, you can post about your page with page link and ask (request) to all the group members to like your page.
**This feature isn't available to all Pages right now.