  We investigate Conjecture 1.6 introduced by Barker and Gelvin in [3], which
says that any source algebra of a p-block (p is a prime) of finite group has
the unit group containing a basis stabilized by left and right action of the
defect group. We will reduce this conjecture to a similar statement about basis
of the hyperfocal subalgebras in the source algebra. We will also show that
such unital basis of source algebras of two p-blocks, stabilized by left and
right action of the defect group, are transported trough basic Morita
equivalences.
