Beyond Birthday (also known as Rue Ryuzaki/B, BB) was the 2nd child taken in at Wammy's House, in an attempt to create a successor for L, and was the serial killer behind the Los Angeles BB Murder Case.
Beyond Birthday has never appeared in the manga, anime, or film series to date, but the BB Case was briefly alluded to in both manga and anime. He was born with Shinigami Eyes, which allowed him to see and know when exactly people around him would die, as well as knowing their full names. He uses this ability to pick his victims and kill them when they would have been destined to die. It is unknown how he could have possibly been born with the eyes, though Mello wonders if a Shinigami dropped its eyeballs to Earth (instead of a Death Note). Some have claimed that Beyond Birthday is a cannibal, but this is only a rumor. The novel did not say anything about him eating his victims' remains. Though this could be true, further information has yet to be revealed. During the investigation of the Los Angeles BB Murder Cases with Naomi Misora, B is described to have jars filled with strawberry jam in the victim's fridge. Some people also speculate that similar to L and Mello's craving for sweets, Beyond Birthday craves strawberry jam. However, he was only said to have eaten an entire jar one time in Another Note: The Los Angeles BB Murder Cases and Naomi Misora never witnessed him doing so again, though she herself wondered about the same thing. It is possible that his love of sweets during the entire time with Naomi Misora was a charade as well. Although mentioned only once in the book, it is also implied that Beyond Birthday practices laughing quite often. Also, it is interesting to note that his laughter is referred to by Mello as a "Shinigami's laugh."
Note: Beyond Birthday exists as a character in the novel "Another Note." The events from this canon Death Note novel occur before the storylines of both the manga and anime.
Little is known about B, though he and A (real name unknown) were the first two children in line to succeed L. The pressure of Wammy's House proved to be too great for A,which caused A to commit suicide, while B wound up running away at some point.
His whereabouts remained unknown from May 2002 to the beginning of the story, L having tracked cases around the world to search for him. Beyond Birthday came up with a plan to surpass L, as the "World's Greatest Criminal", giving L a case that B hoped he would be unable to solve.
Beyond Birthday's first known victim was the freelance writer Believe Bridesmaid, whom he killed July 31st, 2002, after drugging him and then choking him with a rope. Four Wara Ningyo (straw dolls) were left at the crime scene, and in post-mortem mutilation, Bridesmaid's chest was slashed several times; the killer also took the time to re-dress him. When looking at the autopsy photos, Naomi Misora found that the wounds were made to resemble letters (in actuality, a Roman numeral code spelling out the name of the next victim).
The second murder happened four days later, on August 4th. The victim, Quarter Queen (a 13-year-old girl), was also drugged before her death, the cause of which was blunt force trauma to her skull. Her eyes were also crushed in further post-mortem mutilation. Three Wara Ningyo were left at the scene of the crime.
The third killing happened nine days after Quarter Queen's murder. Backyard Bottomslash was a 28-year-old bank worker who had also been drugged before her death, though her age fell in-between those of the previous two victims (44 and 13). This happened when Beyond Birthday wanted to find out if a human can die of an internal hemorrhage without rupturing any organs. Beyond Birthday conducted this experiment by drugging and then beating Backyard Bottomslash's left arm without breaking the skin. When this did not work, her death was caused by loss of blood, with her right leg and left arm cut off. The right leg was discovered in the bathtub later. The left arm was taken by Beyond Birthday. Two Wara Ningyo were found nailed to the walls in a similar manner to the other two cases.
On August 22nd, Naomi arrives at the location where the next BB murder will be committed, and comes to realize that Rue Ryuzaki, the mysterious private investigator she has been working with, isn't what he seems. After figuring out several clues, she finds that Ryuzaki is in fact Beyond Birthday, and that the final murder is actually his attempted suicide. She manages to stop B from burning himself to death, and arrests him.
A year and a half later, on January 21st 2004, Beyond Birthday dies of a heart attack in prison, presumably one of the many criminals killed by Kira. (If the events of this novel are canon to the anime as well, he would have died in 2007).
Throughout the novel, the reader is initially unaware that Rue Ryuzaki, whom Misora thought of as just some suspicious young man, is Beyond Birthday. Readers are led to believe that he is L in person. This is because of his mannerisms and description (black hair, dark bags beneath the eyes, bad posture, love for sweets, and sitting position). It is in fact BB pretending to be L, using his acting skills to pass as a copy of the L he possibly knew or heard about. He had obviously never seen L totally in person, given the fact that he did not know L's lifespan or real name. The undisguised Beyond Birthday is mentioned at points in the novel.
Due to his resemblance to L, it is unknown if the artwork featured in DN:Another Note is Beyond Birthday or L. Some fans believe it to be L, especially since he does not have red eyes, which the fans have begun to connect with Shinigami Eyes. However, it was mentioned in the manga that it is impossible for a human to see if another human has "The Eyes" or not, making Shinigami Eyes appear normal.
Others have pointed out that it is unlikely that there would be two protagonists in the artwork, as opposed to the protagonist as well as the antagonist. In addition to that, there is a distinguishable "B" in between the two characters, implying that the character may very well in fact be Beyond Birthday. However, there is no way of knowing until it is either confirmed or denied by Tsugumi Ohba or Takeshi Obata. His natural eye color is unknown, though the general assumption is that he wears grey contacts to further disguise himself as L.