A method for installing a tubular in a wellbore, comprising: coupling a fluid connector tool to a lifting assembly; coupling a casing fill-up and circulation seal assembly to the fluid connector tool; coupling two segments of casing together to form a casing string, wherein at least one of the segments of casing is fluidically coupled to the casing fill-up and circulation seal assembly; running the casing string into a wellbore; pumping a drilling fluid from the lifting assembly, through the fluid connector tool and the casing fill-up and circulation seal assembly, and into the casing string as the casing string is run into the wellbore; de-coupling the casing fill-up and circulation seal assembly from the fluid connector tool after the drilling fluid is pumped into the casing string; and coupling a drill-pipe seal assembly to the fluid connector tool after the casing fill-up and circulation seal assembly is de-coupled from the fluid connector tool, characterized in that: the method further comprises coupling an adapter to a lower end of the body of the fluid connector tool, wherein coupling the casing fill-up and circulation seal assembly to the fluid connector tool comprises connecting the casing fill-up and circulation seal assembly to the adapter; and coupling the drill-pipe seal assembly to the fluid connector tool comprises coupling the drill-pipe seal assembly to a piston-rod of the fluid connector tool, and wherein the piston-rod is positioned at least partially within a body of the fluid connector tool. coupling a fluid connector tool to a lifting assembly; coupling a casing fill-up and circulation seal assembly to the fluid connector tool; coupling two segments of casing together to form a casing string, wherein at least one of the segments of casing is fluidically coupled to the casing fill-up and circulation seal assembly; running the casing string into a wellbore; pumping a drilling fluid from the lifting assembly, through the fluid connector tool and the casing fill-up and circulation seal assembly, and into the casing string as the casing string is run into the wellbore; de-coupling the casing fill-up and circulation seal assembly from the fluid connector tool after the drilling fluid is pumped into the casing string; and coupling a drill-pipe seal assembly to the fluid connector tool after the casing fill-up and circulation seal assembly is de-coupled from the fluid connector tool, characterized in that: the method further comprises coupling an adapter to a lower end of the body of the fluid connector tool, wherein coupling the casing fill-up and circulation seal assembly to the fluid connector tool comprises connecting the casing fill-up and circulation seal assembly to the adapter; and coupling the drill-pipe seal assembly to the fluid connector tool comprises coupling the drill-pipe seal assembly to a piston-rod of the fluid connector tool, and wherein the piston-rod is positioned at least partially within a body of the fluid connector tool. the method further comprises coupling an adapter to a lower end of the body of the fluid connector tool, wherein coupling the casing fill-up and circulation seal assembly to the fluid connector tool comprises connecting the casing fill-up and circulation seal assembly to the adapter; and coupling the drill-pipe seal assembly to the fluid connector tool comprises coupling the drill-pipe seal assembly to a piston-rod of the fluid connector tool, and wherein the piston-rod is positioned at least partially within a body of the fluid connector tool.