Isn't the cure for the disease of health care inflation the strengthening of the dollar?

No, doesn't work that way. A strong dollar would make the price of internationally-traded commodities such as oil cheaper, and might lower the price of imports produced by foreign labor. But it does nothing to reduce the cost of health care, because the cost drivers underlying health care in the U.S. are priced in those very same dollars and are not based on imports.

In other words, say a doctor in the U.S. makes $300 K a year, a nurse makes $60 k a year, a drug company charges $70 per gram of some drug, some set of procedures costs $20,000, the use of some diagnostic machine costs $X .... all these costs originate in dollars and are priced without regard to whether those dollars happen to be worth more or less Euros or Yen on the currency exchanges.

In short, a stronger dollar would tend to make something cheaper (for Americans) if that thing has built-in costs based on a foreign currency. But that is emphatically not the case for hardly anything in the healthcare industry, where costs are predominantly domestic labor and US-based capital.

No one in our society can give such a permission. The dollar is in the free market and depends on demand and supply. The FED can use some policies to affect the dollar into its favor. But to do that,it will affect the whole economy, not only the dollar.Moreover, if the dollar has gained value, the prices of only import goods will be cheaper, that will cause inflation in the US and higher unemployment. The expensive dollar will also hinder to solve the current account deficit and debts which are our main problems right now.How can it be a cure?

A strong dollar would make the price of internationally-traded commodities such as oil cheaper, and might lower the price of imports produced by foreign labor.

The only cure for health care inflation is competition, i.e., eliminating barriers to entry and ending government subsidies.