He receives dollars from a customer in America to exchange them for pounds in his country, in return for commission

Firstly:

It is
permissible to work as a middleman in currency exchange in return for a set
commission, if you adhere to the Islamic condition of exchange, which is
that the exchange should take place immediately.

The customer in
America can send you dollars for you to exchange for pounds, which you then
send to him, in return for commission. This work of yours comes under the
heading of acting on behalf of someone else in return for a set fee. Thus
you make a deal with the customer in America that you will act as an agent (wakeel)
on his behalf, and you agree with him on your fee.

One of the
conditions of working as an agent is that you should not be liable for
compensation of his money if it is lost or stolen without any act of
transgression or negligence on your part, and that you will exchange his
money for him according to the market price.

Secondly:

You must pay
attention to the condition of exchange, which is that the exchange is to be
done immediately at the time of the currency exchange, because the Prophet
(blessings and peace of Allah be upon him) said: “Gold for gold, silver for
silver, …  like for like, same for same, hand to hand. If any of these types
are different, then sell however you like, so long as it is hand to hand.”
Narrated by Muslim (2970).

Dollars, pounds
and other currencies are separate categories; they come under the same
rulings as gold and silver. Hence it is not permissible to buy one currency
for another unless it is hand-to-hand in the true sense of the word.

Real-time
exchange is also valid, such as if you receive a cheque – either a regular
cheque or certified cheque – or a bank transfer in the currency that it is
to be transferred to, or the money is deposited in the two accounts at the
same time, even if the two parties are in two different countries.

See the answer
to question no. 110938.

You mentioned
two ways of doing the transaction:

1.

As for the first
way, it is not permissible, because there is no immediate exchange, as the
sub-agent takes dollars from you and does not give you pounds in the same
sitting; rather whenever they can collect it from their customer they will
pay you.

2.

As for the
second way, it is permissible. This is where you give them dollars and they
give you pounds within a few seconds, or ten minutes, so long as it is in
the same sitting, i.e., in the same place and time, so you do not leave the
place until you have received the pounds.

Shaykh Ibn Baaz
(may Allah have mercy on him) said: Buying and selling currency is
permissible, but that is on condition that the exchange be done hand-to-hand
if the currencies are different. So if a person sells Libyan currency for
American or Egyptian currency or another type of currency, hand to hand,
there is nothing wrong with that, such as if he buys dollars with Libyan
currency hand-to-hand, so he takes one and gives the other in the same
sitting; or he buys Egyptian currency or English currency, or some other
currency, for Libyan currency or some other kind, hand-to-hand – there is
nothing wrong with that. But if the exchange is deferred, then it is not
permissible. The same applies if the exchange does not take place in the
same sitting; that is not permissible because in that case, if it as
described, then it is regarded as a type of riba-based transaction. So it is
essential that the exchange take place in the same sitting, hand-to-hand, if
the currencies are different. But if they are of the same type, then two
conditions must be met: they must be similar in quantity and must be
exchanged in the same sitting, because the Prophet (blessings and peace of
Allah be upon him) said: “Gold for gold, silver for silver…”[  – and he
quoted the same hadith].

The ruling on
currency is as mentioned above: if it is of different types, it is
permissible for them to be of different quantities, but the exchange must
still take place in the same sitting. If they are of the same type, such as
dollars for dollars, or dinars for dinars, then the exchange must take place
in the same sitting and they must be of similar quantity. And Allah is the
source of strength.

End quote from
Majmoo‘ Fataawa Ibn Baaz (19/171)

And Allah knows
best.