(a) Upon receipt of such application, the board of supervisors of elections shall determine upon such inquiry as they deem proper whether the applicant is a voter legally qualified to vote at such election, and if they find he or she is not so qualified, shall reject the application.
(b) If the board of supervisors of elections shall find that the applicant is a qualified voter as stated in his or her application, they shall deliver to him or her, at the office of the board of supervisors of elections, or shall mail to him or her at an address designated by him or her, an absentee voter's ballot and an envelope therefor. Postage for transmitting ballot material to the voters shall be paid by the city, and postage for the return of ballot shall be paid by the voter. If the ballots are to be sent by mail, such determination shall be made at a time which will afford an opportunity for the transmission and return of the ballots in the usual course of mail, depending upon the location of the mailing address, and which will allow for at least one secular day for marking the ballots, and remailing; but the investigation shall be concluded and determinations made as to all applicants not later than the last Wednesday before election day.
(c) The board of supervisors of elections shall keep a record of applications for absentee voter's ballots as they are received showing the names and residences of the applicants, and a complete list of all applicants to whom absentee voter's ballots have been delivered or mailed shall be available for inspection by any candidate on the ballot or his duly designated agent.