You mean half brother, the mother is the mother of both of them? Does she have full custody of this boy? He can sponsor his mother and they can include the mothers family on her PR application, her dependent children etc. but she needs to have full custody to take the children with her. If she has joint custody with the father of the 4 yo., the father can stop her from taking him out of the country.
The sponsor has to show enough income to support his own family plus the family he is sponsoring. Sponsoring parents generally takes a long time. Approving sponsor, 32 months, see http://www.cic.gc.ca/english/information/times/canada/process-in.asp#sponsorship and PR in Berlin for them, average 14 months, see http://www.cic.gc.ca/english/information/times/international/08-fc-parents.asp#europe so total almost 4 years.
He can start by reading http://www.cic.gc.ca/english/immigrate/sponsor/index.asp
