I have never tried to transplant lichens, per se, but I have successfully introduced them to my garden by bringing in stones that already them growing on them. If you see a lichen-covered rock at a stoneyard or on the roadside near where you live, purchase or scavenge it, handle it delicately, and put it among stones of the same type in your garden. I have been doing this since about 1990, and I have successfully encouraged lichens to colonize sandstone, ironstone, limestone, chert, concrete rubble, and even quartz. Note that these colonize new surfaces at a slow rate. It takes a few years to get new, thriving colonies, and you need to take a mostly hands-, and especially feet-off approach to admiring your rock garden. I find that the lichens are more likely to thrive and spread if they are from somewhere nearby and similar in elevation. I am in Dallas, and my stones with parent colonies came from Texas, Oklahoma, Arkansas, and Louisiana, with a small few from South Carolina, Georgia, Florida, and Alabama. The ones from the Southeast have mostly persisted, but have not thrived as the more local ones have. I have brought back some from California, Oregon, and West Virginia that did not even survive. The most prolific were in some concrete rubble from a pile in a blackberry patch about a mile away. My favorites are the ones growing on quartz—a grey, fluffy one, and a recessed, black one. I bought the stone with the original populations at a stoneyard in McCurtain County, Oklahoma.

The differing opinions above prompted me to conduct my own research. A fungus, an alga, and sometimes cyanobacteria living symbiotically are referred to as lichen. Whether their symbiosis is mutualism or parasitism in its nature is a matter of debate, since the relationship is fairly complex and not yet fully known. As I understand, the relationship is the following (in a very simplified way): the fungus, through its thallus structure and through release of certain beneficial fungi chemicals, provides its photobionts (alga and cyanobacteria) with optimal living conditions. Additionally, fungus absorbs minerals (mainly carbon and nitrogen) from the air and water, and makes them available to its photobionts. In exchange, alga converts carbon to simple sugars which the fungus feeds on, while cyanobacteria provides the fungus with nitrogen, converted to a form the fungus can actually use. Many view the above relationship as mutualism; others argue it’s parasitism, because the fungus consumes more than half the sugars produced by the alga, sugars which the alga also needs for itself. Whatever the case may be regarding the nature of the symbiotic relationship between the lichen-forming organisms, I think it’s generally agreed upon the fact that the lichen does not parasitize the substrate it lives on; so it won’t harm a tree or other thing it attaches itself to, because it doesn’t feed on that substrate. My question was whether or not anyone could tell me if it’s a moss or a lichen, and perhaps even identify it by its name. However, I’m glad the discussion took this turn, because I’ve now gained a great deal of appreciation for lichens. Still, if anyone happens to know the name of this particular lichen, please let me know. Thanks everyone.

Not worth the effort even thinking about it, much less going through the trouble of trying to strip it off. Which may be likely to cause troubles for the host plant anyway. Lichen is completely harmless to whatever host it might be growing on - rocks, fences, cars (yes, I have had lichen growing on my ungaraged car roof) and trees and shrubs. I could show you entire lichen forests in my area but they are really only very visible in winter when the trees are leafless. Rainfall is not a significant factor in their formation. There are lichen that grow in deserts.

the one with oragne flowers appears to be a variety of - perhaps - misletoe; but the flowers in CA are white. This is probably a form of parasitic plant common to your area.