Fuku first appeared in the episode "Neju Who?" She is a "cabbit," a small, part rabbit, part cat-like creature that hatched from an egg in the Kamidake II, the ship of GXP main protagonist, Seina and was given her name by Seina himself for the Japanese name for good luck, the complete opposite of Seina himself who is notorious around the galaxy for his bad luck. She is the younger sister of Ryo-Ohki, the extremely powerful cabbit/spacecraft of space pirate Ryoko created by Washu. Fuku has a great love for her creator/mother, Washu and has fond memories of her even before hatching.
Washu created Fuku on the request of Tenchi, who was worried about the safety of his extremely unlucky friend Seina in the Galaxy Police.
One thing to note, is that the cabbit appearance of Ryo-Ohki resulted from Ryoko integrating the remains of Chibi, a little cat she had been keeping alive for Tenchi before he released her at the beginning of OVA 1. So while Ryo-Ohki's appearance is a side-effect of the integration, Fuku's was modeled after the integrated Ryo-Ohki.Like Ryo-Ohki, she is the biological computer unit and, at first, the principle power source of the Kamidake II, which can fluctuate depending upon the mood of Fuku. Her appearance is identical to her sister's when she first hatched in the 3rd episode of the OVA. One characteristic that distinguishes her from Ryo-Ohki is the small bell on her neck which she received from Seina. She later shared responsibility for the Kamidake when Kiriko Masaki Jurai was bonded to second-generation Royal Tree, Miyuki, which gave Fuku help in powering the ship to battle against the Unko of the Good Luck Fleet. She also shares her big sister's love of carrots. Washu also explained to Seina, that with proper raising and nurture, Fuku will be able to transform into a humanoid form like Ryo-Ohki can.
Fuku, as well as the Kamidake II, were also briefly taken away by a corrupt faction of the Galaxy Army that were aiding Shank in order to analyze her for their own personal desires and placed her into a stasis field. The G.A. scientists attempted to clone Fuku, but could only produce five imperfect clones. Eventually Seina was able to rescue Fuku, as well as the clones. As for what happened to the clones are unknown.
Towards the end of the series, Seina's crew and the girls who vy for his affection, Amane, Ryoko, Neju, and Kiriko were later engaged to wed Seina in a political marriage. And as the Kamidake II now falls completely under Seina's control, with Fuku as a part of the ship, Seina in a way was marrying Fuku as well.
Fuku also made a brief appearance in Tenchi Muyo! Ryo-Ohki,, when at the end of the final episode of OVA 3, she travels back to that time period from an unspecified point in the future, alters the message to Mihoshi Kuramitsu's family (that antagonist Z had originally altered in the original timeline) in order to put the timeline in correct order, so that she would eventually meet Seina. Fuku was accompanied by a slightly older version of Noike, who also didn't want the timeline adversely affected so that she would be able to meet Tenchi.
Fuku's relationship with Seina is very similar to Ryo-Ohki's relationship with Tenchi . Fuku is deeply devoted to Seina, and that devotion is clearly demonstrated by her willingness to help him, despite the fact that sometimes she can be easily frightened. Her personality is also very similar to Ryo-Ohki in the sense that she is very sensitive and desires to be loved and showed affection by others; and when she is sad and lonely, she easily becomes depressed. Seina was also the first one to truly care for her when he demonstrated his faith in her.Fuku also has a good relationship with Neju Na Melmas and hangs around with her when she is not with Seina, which is similar to Ryo-Ohki's relationship with Princess Sasami in the original series.
As a result of her relationship with Seina, Fuku has demonstrated to be very powerful whenever Seina or anyone else is in danger, which has lead to her mood and feelings supplying immense and powerful energy to the Kamidake II whenever its crew were in danger.
Fuku is not nearly as powerful as Ryo-Ohki, as the elder cabbit's power stems from the gems of Washu, who placed all of her godly power in them while Fuku's power doesn't.In GXP episode 17, Washu revealed that like Ryo-Ohki, Fuku too can shapeshift into a humanoid form but she has to want to. Washu also tells Seina that she needs nurturing before she can perform the task.
Additionally, Fuku, along with Noike, appeared in the final scene of Episode 6 of the third Tenchi Muyo! OVA, making sure the letter to Mihoshi's family (originally altered by Z) got through, with Fuku doing the typing.