Strengthening America's Strategic National Stockpile Act of 2020 This bill makes changes to the administration and management of the Strategic National Stockpile. Among these changes, the bill authorizes through September 30, 2023, the Department of Health and Human Services (HHS) to transfer supplies from the stockpile to any federal departments or agencies under certain conditions. HHS must also ensure the contents of the stockpile remain in working order and may enter into maintenance service contracts to carry out this requirement. Furthermore, as part of its management of the stockpile, HHS must establish and maintain domestic reserves of certain supplies, including by entering into cooperative agreements or partnerships to access facilities and equipment to produce these supplies. The authority for such agreements and partnerships terminates on September 30, 2023. Additionally, the bill temporarily authorizes HHS to award grants to states for maintaining stockpiles of certain equipment and supplies for use during public health emergencies. HHS must also develop transparent processes for the use and distribution of supplies from the stockpile that address, for example, the prioritization of requests. Additionally, during the COVID-19 (i.e., coronavirus disease 2019) emergency, the Office of the Assistant Secretary for Preparedness and Response must report monthly on requests for supplies from states, tribes, and other jurisdictions. These reports must include the rationale for any partially fulfilled or denied requests. Lastly, the Government Accountability Office must study the feasibility of establishing user fees to offset costs for procuring single-source materials for, and distributing such materials from, the stockpile.