Samantha Lewthwaite's clumsy poem, littered with spelling mistakes, was found by British police investigators after they examined a computer hard drive found at a house in the Kenyan town of Mombasa, Britain's Sky News television said.
"Oh sheik osama my father, my brother / My love for you is like no other / Oh Sheik Osama now that you are gone / The muslims must wake up they must be strong," it begins.
It continues, "Al-Qaeda are stronger and fiercer than ever / Thinking in the end you are stupid it will NEVER / Be over until the day that we see our lands returned and governed by He Allah the almighty,/ Whose law is complete.
"So make your plans and He is the best of planners./ Their was no victory for you Mr (US President Barack) Obama / The honour is his on martyred Osama!!!!!!!!!!!!!!!!"
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Lewthwaite is the widow of Germaine Lindsay, one of four Islamist suicide bombers who attacked the London transport network on July 7, 2005, killing 52 innocent people.
The notice did not specifically mention the mall siege, saying instead that Lewthwaite was wanted on charges of being in possession of explosives and conspiracy to commit a felony dating back to December 2011.
Investigators also found a flash drive believed to belong to Lewthwaite which showed how she spent eight years researching bomb making, Sky News said.
The report said that the hard drive led investigators to a three-bedroomed flat in Nairobi overlooking a shopping centre similar to the Westgate mall attacked last month.
The hard drive also contained several photographs of Lewthwaite, which reveal she spent much of her time on websites concerning body image.
One site she viewed showed how to obtain a hairstyle like US singer Taylor Swift, others had details on dieting and another offered an online course of self-defence.