How can Pyridostigmine have the indication of Myasthenia?
Pyridostigmine is an analog of neostigmine, so has the same basic mechanism of action. Please forgive me for repeating information you may already know.

There are two main families of acetylcholine receptors: muscarinic and nicotinic. Acetylcholine receptors at the neuromuscular junction (NMJ) are exclusively nicotinic (N1 or NM), so that's the only receptor I'll address.

Myasthenia Gravis is caused by an immune response to nicotinic postsynaptic receptors on skeletal muscle. An antibody can either destroy or block the receptor site. The antibodies destroy the receptor sites more rapidly than the body can replace them. In MG, there can be as much as an 80% reduction in the number of these receptor sites.

Acetylcholinesterase (AChE) is an enzyme that breaks down acetylcholine (ACh) at the synaptic cleft. AChE has a remarkably high specific catalytic activity: each molecule of AChE degrades about 25000 molecules of ACh per second. Any drug which serves to inhibit AChE will increase ACh concentration at the N1 receptor. AChE inhibitors can be irreversible or reversible. Reversible inhibitors, (competitive or noncompetitive) have therapeutic applications; irreversible AChE  modulators are toxic. 

Carbamates are organic compounds derived from carbamic acid (NH2COOH). They are reversible AChE inhibitors. This group includes neostigmine, pyridostigmine and physostigmine. Pyridostigmine is an analog of neostigmine, so has the same basic mechanism of action. Because they are not lipid soluble, they are selective for the NMJ; both also have direct action on Nm Receptors. The major difference between them is that pyridostigmine has a slight but significantly longer duration of action.

Drug Bank: Pyridostigmine
NeuroLex.org (get's it's info from PubChem)