Puerto Rico Small Business Contracting Assistance Act of 2018 This bill amends the Small Business Act to double for four years after its enactment the value of a prime contract awarded by a federal agency to a small business with its principle office in Puerto Rico in order to comply with the Act's governmentwide goal for small businesses' participation to be at least 23% of the total value of all prime contract awards for each fiscal year during such period. Beginning on enactment of this bill and until the termination of the Financial Oversight and Management Board, the Small Business Administration (SBA): may transfer technology or surplus property to a Puerto Rico business if it meets SBA requirements for such transfer, without regard to whether the business is a small business and capital ownership development program participant; and shall identify potential incentives to a covered mentor that awards a subcontract to its covered protege (i.e., positive consideration in any past performance evaluation of such mentor, the application of costs incurred for providing training to the protege to the mentor's subcontracting plan, and such other SBA incentives). The bill requires the SBA to allow up to two additional mentor-protege relationships for protege firms that are Puerto Rico businesses. (Currently, the limit on SBA mentor-protege relationships is three.)