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I am sorry to learn of this dispute, but fortunately this is relatively easy to settle.
The HOA documents will identify what spaces are part of the "common area" and what is part of the "separate interest".
You may have to look in a couple of different places (this can include the Articles of Incorporation, By-Laws, CC&Rs, or Deeds, there may be others). But there will be very specific documentation showing what belongs to the HOA, and what belongs to the individual owners.
The spaces cannot belong to both, and it will not be vague.
Unfortunately, if the seller (the person you bought your property from) was wrong, and the spaces really do belong to this other owner, you will not have recourse against the seller because these documents are available to the public (they are so open and public that the seller cannot keep them secret, and any representation that they make can be easily verified by checking these public documents).
But if this other owner, now president, is making a "land grab" and trying to claim ownership, you can easily present these recorded documents showing that the property belongs to the HOA as "common area" and is available for use under the terms of your governing documents.