exchange rate and domestic money supply part II This question is related to the answer to the question
exchange rate and domestic money supply 

It is said that the 'CB purchases foreign currency on currency market'. 

Is it possible that some of this purchasing is even done within the domestic market (I would guess not but don't really know)? Or are we assuming that in circulation means within the domestic market and foreign market (again I would guess not)? Or is maybe that we assume/know that when in circulation, our currency will find its way back to our market and this will obviously result in more money in circulation. Maybe I am really thinking about it in the wrong way, and in circulation simply means that there are lenders out there now (foreign or domestic) that have more of our currency and will lend at a low interest rate.
@Toby comments noted, I will attempt an answer.  First, the FX market is international so you cannot tell whether the foreign currency seller is domestic or foreign. However, if it is a foreign buyer, they will typically reinvest the dollars in either a commercial or financial asset such as a Treasury bond, which could result in the remittance of the dollars back to a domestic holder.   What you know for sure is that the dollars will be deposited in a bank somewhere and will add to the pile of excess reserves currently held by the US banking system.  Hence technically the money supply goes up.  

Perhaps the greater question is whether raising the money supply in this way has any effect on the economy.  I would suggest not, since banks already have excess reserves.   Rather, the transmission mechanism for FX intervention is via changes in the exchange rate.   But that could be debatable.