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If you take buttermilk and some moss, then blend it up (in an old blender you don't intend to use for food), you can then spread this on the object you want to have moss grow on.

The buttermilk help provide the additional acidity the plant likes and the moss pieces will "regrow" to cover the whole object.

It is either moss or lichen. Either way it is harmless, but if you want to get rid of it, here is some information: https://www.gardeningknowhow.com/ornamental/fungus-lichen/treatment-tree-lichen.htm
https://www.gardeningknowhow.com/ornamental/foliage/moss/moss-on-plants.htm

This article will help you: https://www.gardeningknowhow.com/ornamental/foliage/moss/killing-moss.htm

This article will help you with that:
https://www.gardeningknowhow.com/ornamental/foliage/moss/moss-on-plants.htm

Here is an article or two that you may find helpful: https://www.gardeningknowhow.com/ornamental/foliage/moss/moss-on-plants.htm
https://www.gardeningknowhow.com/ornamental/foliage/moss/killing-moss.htm

Moss will happily grow where many other plants will not, like shade. Since moss will grow nearly anywhere and in any soil type (provided the pH is 5.0-6.0), they’re relatively easy to transplant from one part of the landscape to another. Spring or fall is the best time for planting moss, especially after it rains. Prepare the site by removing any grass or debris and raking the area smooth. Water it thoroughly and then place the moss, in patches, into the designated areas, pressing down firmly. You can also moisten the bottoms of the moss. There’s no need to keep them close together. Once it has taken hold, the moss will readily spread into one another, filling in any empty gaps. To help the pieces of moss stay in place, secure them with small twigs. Keep the area damp, but do not over water. The moss patches should begin to establish themselves within a month or so. Moss also propagates by spores so putting it in a blender with water or buttermilk for a minute or two and pouring it onto the area will also create healthy moss plants in about five weeks.

This article may also help: https://www.gardeningknowhow.com/ornamental/foliage/moss/growing-moss-gardens.htm