We report on Hubble Space Telescope Faint Object Spectrograph observations of the double QSO HS 1216+5032 AB ( z _ { e } ( { A } ) = 1.455 ; z _ { e } ( { B } ) = 1.451 , and angular separation \theta = 9 \aas@@fstack { \prime \prime } 1 ) . The spectral coverage is 910 Å to 1340 Å in the QSO rest-frame . An unusual broad-absorption-line ( BAL ) system is observed only in the B component : maximum outflow velocity of \sim 5 000 km s ^ { -1 } ; probably a mixture of broad and narrow components . Observed ions are : H i , C ii , C iii , N iii , N v , O vi , and possibly S iv and S vi . We also discuss two outstanding intervening systems : ( 1 ) a complex C iv system at z = 0.72 of similar strength in A and B , with a velocity span of 1500 km s ^ { -1 } along the lines of sight ( LOSs ; LOS separation : S _ { \bot } [ z = 0.72 ] \approx 75 ~ { } h _ { 50 } ^ { -1 } kpc ) ; and ( 2 ) a possible strong Mg ii system at z = 0.04 observed in B only , presumably arising in a damped Ly \alpha system . We assume HS 1216+5032 is a binary QSO but discuss the possibility of a gravitational lens system . The size of Ly \alpha forest clouds is constrained using S _ { \bot } \approx 80 ~ { } h _ { 50 } ^ { -1 } kpc at redshifts between z = 1.15 and 1.45 . Four Ly \alpha systems not associated with metal lines and producing lines with W _ { 0 } > 0.17 Å are observed in both spectra , while five appear in only one spectrum . This sample , although scarce due to the redshift path blocked out by the BALs in B , allows us to place upper limits on the transverse cloud sizes . Modelling the absorbers as non-evolving spheres , a maximum-likelihood analysis yields a most probable cloud diameter D = 256 ~ { } h _ { 50 } ^ { -1 } kpc and 2 \sigma bounds of 172 < D < 896 ~ { } h _ { 50 } ^ { -1 } kpc . If the clouds are modelled as filamentary structures , the same analysis yields lower transverse dimensions by a factor of two . Independently of the maximum-likelihood approach , the equivalent width differences provide evidence for coherent structures . The suggestion that the size of Ly \alpha forest clouds increases with decreasing redshift is not confirmed . Finally , we discuss two z _ { a } \approx z _ { e } Ly \alpha systems observed in both QSO spectra .