  The definition of the grafting operation for quasifuchsian groups is extended
by Bromberg to all $b$-groups. Although the grafting maps are not necessarily
continuous at boundary groups, in this paper, we show that the grafting maps
take every "standard" convergent sequence to a convergent sequence. As a
consequence of this result, we extend Goldman's grafting theorem for
quasifuchsian groups to all boundary $b$-groups.
