Nabeelj is correct. I called and confirmed,

1) Sears Club Points from Sears Card can be converted to Petro points.
2) Sears Club Points from Sears MasterCard can only be converted to Reward Partners' Gift Cards, and not to Petro Points.
3) As of Feb. 1, Sears Card's holders will be offered to upgrade to Sears MasterCards. But this "upgraded" MasterCard's Sear Club Points can not be converted to Petro Points either.

In other words, it's no go for me. So, I asked my application for Sears MasterCard be cancelled.