We recently moved into this home and it's nestled in the forest for the most part so our yard is very shady. We have a large sheet of moss near the front of the house that I'd like to nurture and spread. In doing a little research this morning it looks to be haircap or star moss. Some of it is very green but some of it is brown and looks dead. I haven't done anything with it yet but would like to get advice on what to do to nurture it back?

I would also like to transplant some of it to other areas of the yard so it could possibly spread. Would it do this?

When you transplant the moss you have to match conditions as close as you can to be successful.

Mosses are encouraged by low fertility, acid soils, and compacted soil. These are things that most plants generally dislike, and so the moss has less competition, and won't get overrun by taller plants.Soils can be be dry or wet, shaded or in sun, which can determine which mosses will thrive. Mosses don't have roots like regular plants, so soil depth isn't important, as long as the moisture retention that the species needs is there.

If you think you have found a suitable place, you can take 4-6 inch (minimum) diameter patches and transplant them. Take a layer like a pancake or biscuit that includes a quarter inch of soil. More soil is fine, but it is not needed. Transplant to the new location, placing it at the same level as before. Do not put soil on top! Water with water that is neutral or acid (pH 7 or less). Do not water with city water. If you have a well, that should be fine, or you can use distilled water, creek or lake water, or rain water. This first water should be all it needs. If it likes it there, it will thrive. If it dies, then mostly likely any further attempts will fail also.