When analysing the transfer you need to look at both sides of the balance sheet. Specifically, a transfer between banks always consists off assets and liabilities that net each other out. For example, when you make a tansfer from your bank account in the US to that of someone else in the US. The bank will tansfer the credit in form of a liability (from its balance sheet to the balance sheet of the other bank) and an asset (it will transfer reserve money of the same amount).
The process is similar for international transfers. The transfer will show up as a liability on the balance sheet of the bank in Singapore (because it is a credit to Crook Island). This needs to be offset by an actual asset that has to sent by Crook Island and to be received by the Bank in Singapore. If the account in Singapore is in US\$, then Crook Island has to somehow send actual US\$ in the amount of the transfer. To do that, the Crook Island bank needs to have actual US$ cash or assets that can be converted into US\$, which it then has to send.
Obviously, you can make the case more convoluted, for example involving the Crook Island Central Bank (if there is any) or the Bank for International Settlements (BIS), or even adding on top various interbank transfers at home or abroad, but ultimately it boils down to the simple mechanism above. For example, the BIS wouldn't send money to Singapore on Crook Island's behalf if there were not some Crook Island assets backing it.
So, from the Singaporean bank's perspective, there is no issue with a transfer from Crook Island, because Crook Island has to actually transfer assets (a loan to Crook Island is a different story, but that was not the question). From Crook Islands perspective it's probably difficult to detect the fraud in the local bank. Someone would have to go and look very closely at the balance sheet and evaluate any assets that are claimed to back the "forged bank money". The two sons would probably prevent this.
Incidentally, the requirement of the mechanism described above is one reason why North Korea doesn't forge bank money, but actual US\$ banknotes! It sells them at a discount for real ones, which it can then use to make transfers abroad (for example, when it imports something).