Check your coin.
There were no Two Pound coins issued in 1945 and, Queen Elizabeth II was not crowned until 1953.
A 1962 Canadian silver dollar with the image of Elizabeth and text of ELIZABETH II DEI GRATIA REGINA is worth $11.42 today. This is because of the value of the metals used to make the silver dollar.
wht the value
The Latin phrase "Dei Gratia Regina Elizabeth" translates as Elizabeth, queen by the grace of God. This phrase (or an abbreviated version, D. G. Regina) appears on all the coinage of the British Commonwealth, therefore it does not identify a specific coin. I don't even know what country it is from, let alone what its denomination is. Furthermore, even if I knew exactly what coin you were talking about, the value varies tremendously depending upon the condition of the coin. Most coins from 1958 would have no value to a collector unless they were in extremely good condition.
Please post a new question with the coin's date. As a rule of thumb, anything dated 1971 or later is worth only face value. Note that the phrase "Gratia Regina" is part of a longer Latin motto that's on ALL English coins, so it doesn't identify one from another.
Canada issued 6 different circulating coins in 1960. Please post a new, separate question with the coin's denomination.
Elizabeth 11 Regina silver 50 cents
http://www.ukcoinpics.co.uk/qe/sov/s66.jpg it is a 1 pound coin this should get you to the right place.
....You need to give us the denomination and the country of origin for the coin. All you told us is that a coin minted in 1965 with Elizabeth II's face on it (and all Dei Gratia Regina FD means is basically By the Grace of God Queen and Defender of the Faith).
The value for a well preserved one could be around $250- $300.
The coin is worth very little, maybe £1 if it was in absolute mint condition. Any value would be associated with the necklace.
1 pound
It's a common circulation coin with no special value. Note that ALL British coins have variations on the motto Dei Gratia Regina Fid Def ... so that's not an identifying detail.