Transforming SHA-512 into SHA-512/256?
Like Richie Frame commented, as SHA-2 padding uses the length of the message that is not possible. Specifically, even if you had some string of input that took you from the SHA-512 IV to the SHA-512/256 IV, any message you hashed with it prepended would have a different length and thus a different hash value.

Additionally, even ignoring the padding it would be infeasible to find such a string. The IV constants for SHA-512/n have been chosen using an algorithm that does not start with the normal SHA-512 IV, so it would require a preimage attack on the compression function to find one.

However, unless you need compatibility or conformance with SHA-512/256, you could just use SHA-512 and truncate. See page 27 of the FIPS document you linked.