Broadly speaking, the Forex market is a place where one can buy and sell currencies and on this market every deal is a currency transfer although the money itself does not move physically. The Forex market offers extreme liquidity which attracts many market players, often called brokers and dealers, but most of them are there to benefit from the opportunities of a well developed marketplace and rarely offer currency transfer services in the sense that they do not provide money transfer services.
Obviously, one enters a particular market to earn a profit and that is exactly what brokers and dealers do. In general, Forex dealers and brokers use spreads to do so: by collecting the difference between the buying price and the selling price, namely the "spread".
Forex dealers in any country are subject to close supervision by one or more government regulatory bodies and usually pay very high fees for the right to be involved in the foreign currency exchange trade. Usually, a Forex dealer plays on the market using his own account, while Forex brokers act as intermediaries between their clients and the market, acting as agents on behalf of the client. There is also a third interstitial category of foreign exchange dealers called "broker-dealers" who act as both brokers and principals.
This great specialisation and the nature of the Forex market prevent some brokers and dealers from engaging in currency transfers, limiting their activities to currency trading. One would argue that it is easy for a broker, individual or institutional, engaged in the foreign currency exchange business to also conduct currency transfers. This appears to be true only on the surface. In reality, currency transfers abroad are subject to different regulations and often are supervised by a different government body so a broker or a dealer must also have expertise in this market niche to obtain all the necessary licences and to be familiar with the respective legislation. Thus, not all Forex dealers and brokers are willing to offer such services.
Moreover, some dealers prefer to specialise in niche markets such as exotic currencies; therefore, they can offer their clients favourable currency exchange rates against a particular not widely known currency and even to provide a currency transfer service but they have limited resources when the transaction in question is to provide a full-scale service covering more than several currency pairs.
Selecting a good Forex dealer and a good currency transfer company, respectively, could be a complicated task. Presumably, in such a tightly regulated market there are no market participants whose primary goal is to deceive you but it will help to check if a particular dealer is experienced in exactly the types of services you are looking for.