I got the option to make the wedding ring from Ash by unlocking all the side memories. Meaning, I paid a good amount of regular chips to buy the partial memories, and bought ALL the quartz shards available in the shops. I think there's actually two quartz shards available in the Alien Faction Shop. But you unlock the second quartz shard after finding out the true identity of the 'Alien Chieftain' dude.
It's been a while since I last played this old gem. Hope I got all that right lol