He has three known addresses, in Malvern, in West Chester, and in Philadelphia. He also goes by the name Zahid Abdul-Muqueek.
Police say Goodman was observed buying some items, while pocketing others by security on Sunday.
He was confronted outside the store by Jefferies, who then took Goodman inside his security booth for questioning.
"They walked inside, seemingly no problem between the two parties. When they get behind the closed door of the security desk, the security guard tells him he needs his name, his date of birth, he's not going to be permitted in the store anymore," said Lt. John Walker of the Philadelphia Police.
Police say Goodman started taking items out of his pockets and placed them on the counter. Then, police say, Goodman pulled out a gun and fired three times at Jefferies' head, hitting him in the head and shoulder.
Goodman then walked out of the store calmly, police say, and left the area.
Jefferies is now listed in fair condition. He spoke by phone with Action News Monday afternoon, saying ""I feel better, I have my complete memory. I'll be fine."
After surveillance video of Goodman leaving the store was made public, police say they receive two tip calls about Goodman's identity.
Police say Goodman was trying to shoplift dental floss and cologne after being sent there by his ailing grandmother to do some shopping for her.
Goodman is considered to be armed and dangerous.
The Citizens Crime Commision is putting up a $2,500 reward for information leading to the arrest and conviction of Goodman, anonymous calls can be place at 215 -546-TIPS.
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