The mechanism of expression of GFP at the exosome surface is currently not available. The public data sheet describes that the exosomes express the fluorescent protein GFP on the surface of their membrane, to allow their detection by instruments equipped with green fluorescence detectors, e.g. 488 nm laser. Please see the link below to review the product datasheet:
https://www.sigmaaldrich.com/deepweb/assets/sigmaaldrich/product/documents/351/804/sae0193pis-ms.pdf
In addition, the following references may also be of interest:
Extracellular vesicles: exosomes, microparticles, their parts, and their targets to enable their biomanufacturing and clinical applications
https://www.sciencedirect.com/science/article/pii/S095816691830140X?via%3Dihub
Shedding light on the cell biology of extracellular vesicles
https://pubmed.ncbi.nlm.nih.gov/29339798/
The biology and function of exosomes in cancer
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4811149/
EV-TRACK: transparent reporting and centralizing knowledge in extracellular vesicle research
https://www.nature.com/articles/nmeth.4185
The generation and use of recombinant extracellular vesicles as biological reference material
https://www.nature.com/articles/s41467-019-11182-0