Suica card issued by JR East Japan can be refunded at JR East Stations, while Suica card issued by Tokyo Monorail or elsewhere cannot be refunded in JR East Stations. Suica Cards are issued by three different companies.
You can "return" a Suica Card to the issuer only.
(Legally, a Suica Card is "lent" to you by the issuer.)
E-money stored on a Suica Card can be valid for 10 years after you use the card last.
If you can later visit a Tokyo Monorail office in Haneda Airport International Terminal Station to refund the e-money,
the quickest way for you to obtain a Suica Card is to get a Monorail Suica Card issued by Tokyo Monorail just before your first ride.
(You can ask a Tokyo Monorail attendant in the station where a Monorail Suica Card is available.)
I am arriving at Haneda Airport around 6am. JR East Travel Service Center in Haneda Airport International Terminal Station (of Tokyo Monorail) is open only from 7:45.
The JR Ticket Office (called "Midori-no-madoguchi") in Hamamatsucho Station is open only from 8:00.
If you clear the immigration procedure much earlier than 7:45,
probably your earliest chance to purchase a Tokunai Pass would be at a reserved-seat ticket vending machine in Hamamatsucho Station.
(1) Get a Monorail Suica Card issued by Tokyo Monorail.
(2) Take a Tokyo Monorail train with your Suica Card from Haneda Airport International Terminal Station to Monorail Hamamatsucho Station. (Fare: 483 yen.)
(3) Get from Monorail Hamamatsucho Station: South or Central Exit to South Gate: Hamamatsucho Station via the transfer passage.
- Tokyo Monorail: Monorail Hamamatsucho Station
http://www.tokyo-monorail.co.jp/english/guidance/hamamatucho/index.htm...: A photo of the transfer passage appears when you click the sign "to JR Line" on the map.
(4) Find a ticket vending machine of this type.
http://www.jreast.co.jp/mv-guide/demo/img/kenbaiki.gif(5) Touch "English" button on the panel, select the category like discount tickets then purchase a Tokunai Pass, which may be described as a Tokyo Metropolitan District Pass.