In this case the task is simply to construct a shortest possible game ending with the given position.
When published, shortest proof games will normally present the solver with a diagram - which is the final position to be reached - and a caption such as "SPG in 9.0".
They can present quite a strong challenge to the solver, especially as assumptions which might be made from a glance at the initial position often turn out to be incorrect.
For example, a piece apparently standing on its initial square may turn out to actually be a promoted pawn (this is known as the Pronkin theme).
A number of chess problem composers have specialised in SPGs, with one of the most notable examples being Michel Caillaud who did much to popularise the genre in the 1970s and 1980s.
It is a version by Andrei Frolkin of a problem by Ernest Clement Mortimer, and was published in Shortest Proof Games (1991).
The problem may carry a stipulation similar to "Find a game with 8.b7-b8=N mate", which simply means a game must be constructed starting from the initial position and ending on the given move number with the given move.
Or it may be a one-sided proof game, in which only white makes moves (this is the SPG analogue to the seriesmover in other types of chess problems).
An SPG-type problem is to find the shortest game in which White's and Black's corresponding moves are mirror images of each other.