The Brother PES file format is quite complex, and I was able to decrypt only version 1.0 completely (which is required for writing a file; higher PES versions can be read, but not written).
Unfortunately PES v1.0 has a size limitation of 5" x 7" (130 mm x 180 mm) and doesn't hold any hoop information. StitchBuddy is assuming the smallest fitting Brother hoop when opening a PES file, showing it just for an easier alignment, but there is no way to save a hoop selection due to the file restriction.
There might be a bypass, depending on the capabilities of your embroidery machine: Many Brother machines are accepting DST designs, without any size limitation. So you might be able to stitch out larger files - even if it requires additional steps / efforts and is only acceptable for a small number of files. Please refer to this FAQ article "PES size limitations" for more instructions…