The exact item name is Production Device: HP Recovery. We need to type in the name correctly to find it in the personal shops. Still on ship 1, only about a dozen shops are selling it. Maybe it's hard to find on less populated ships.
As Rang Dipkin commented, this item drops as a reward of Emergency Trials, just that the drop rate is extremely low. So I don't think there's some reasonable way to farm it. I suppose some of the level up quests, like "The Silence Born of Chaos" or "Chaos, Render of Tranquility" have emergency trials frequently. But I'm not sure if playing these quests all the day would drop this device.