Unitification of weakly Rickart and weakly p.q.-Baer *-rings

S. K. Berberian raised the problem ``Can every weakly Rickart *-ring be embedded in a Rickart *-ring with preservation of right projections? ". Berberian has given a partial solution to this problem. Khairnar and Waphare raised a similar problem for p. q. -Baer *-rings and gave a partial solution. In this paper, we give more general partial solutions to both the problems.