Catalyzes the reaction that attaches fucose through an O-glycosidic linkage to a conserved serine or threonine residue in the consensus sequence C1-X-X-S/T-C2 of thrombospondin type I repeats (TSRs) where C1 and C2 are the first and second cysteines of the repeat, respectively (PubMed:28916755). O-fucosylates sporozoite proteins CSP and TRAP (PubMed:28916755). O-fucosylation regulates stability and intracellular trafficking of TRAP but not of CSP (By similarity). Probably by regulating protein O-fucosylation, may play a role in parasite transmission to the mosquito vector and/or infection of the vertebrate host hepatocytes; however, POFUT2 involvement in transmission/infection is controversial (By similarity). GDP-beta-L-fucose + L-seryl-[protein] = 3-O-(alpha-L-fucosyl)-L-seryl-[protein] + GDP + H(+) GDP-beta-L-fucose + L-threonyl-[protein] = 3-O-(alpha-L-fucosyl)-L-threonyl-[protein] + GDP + H(+) Protein modification; protein glycosylation. Belongs to the glycosyltransferase 68 family.