If the fungus spreads out from plant to planet, say on the voyager spacecraft or from meteorites and asteroids then it can replicate.

The fungus might need to evolve humans to create spacecraft to send itself to new planets and places.

It certainly has traveled to all 6 continents. 

https://www.researchgate.net/publication/12312068_Evolution_Terrestrial_life--fungal_from_the_start

https://open.lbry.com/@Permaculture:e/radical-mycology-with-peter-mccoy-a:d

https://odysee.com/@R-Future-Our-Regenerative-Future:d/Day-3-Mycology---The-Future-with-Peter-McCoy:9?&sunset=lbrytv

https://www.science.org/doi/10.1126/science.aab1161

https://onlinelibrary.wiley.com/doi/10.1002/pld3.369?af=R

https://friedmanlab.oeb.harvard.edu/files/friedmanlab/files/2009_winther_friedman_psilotum_nudum.pdf

https://pubmed.ncbi.nlm.nih.gov/30253017/

There have been horizontal gene transfers between the fungus and the plants and bacteria it lives with.

https://www.frontiersin.org/articles/10.3389/fpls.2018.00701/full 

"In addition, the MRE genomes harbor genes horizontally acquired from AMF" The bacteria inside the fungus has its dna modified by the fungus. https://pubmed.ncbi.nlm.nih.gov/25964324/

"However, evidence strongly suggests that nuclei can be genetically divergent within an AMF individual." https://pdfs.semanticscholar.org/4a52/65e582620cbc633cff8fb1a197859be124c0.pdf that means its true the dna is different inside a single fungi

The basic idea here is that the AM fungus could possibly contain dna samples of many lifeforms it encounters and would act as a living genebank and able to inject dna into other cells directly.