Once syphilis enters its third stage it is no longer curable, is that true

False.
all stages are curable with proper medical attention.

It's curable, the first sign of syphilis is a small sore and it appears after the infection. Symptoms appear in about 3 weeks. In it's second stage, rashes on other parts of the body begin to appear. The third stage can last up to multiple years. It can, in fact, be treated in this stage but it is much, much smarter to treat it in the first two stages.