A recipe that calls for a cup of molasses almost certainly needs the liquid. A blend of corn syrup and molasses would probably work.
For the record, the pre-industrial method of producing sugar was to boil cane juice, then put the almost solid sugar into an inverted cone. Molasses dripped out the bottom, and what was left was a solid cone of brown sugar. You then refined that a second and again a third time to separate the molasses from the white (expensive) sugar.
It is stronger (blackstrap) depending on which refining it dripped from.
Modern molasses lacks the edge that blackstrap has, most people prefer it to blackstrap.
Modern brown sugar is made by mixing a small amount of molasses into refined white sugar.
Natural food stores sell unrefined or raw sugar, taste and use similar to brown sugar.
I'm not certain what granulated molasses is.
I've never seen or heard of 'granulated molasses'. What's brand and product description? The only thing I can think of is that someone took the raw sugar that is sold in cones or blocks in Hispanic groceries, and ground it up. In effect, very dark brown sugar.
It might work to dissolve this molasses in some water (probably boiling), trying make as thick a solution as possible. But for a cake like this, substitution could be tricky.