I have an English translation of the letter; you can find my email address on my homepage.
Here is the relevant part:

"By the way, I take it to be not useless to note down also such propositions
that are very probable, even if a real proof is lacking; for even if
afterwards they were found to be erroneous, they could all the same give
occasion for the discovery of a new truth. Thus Fermat's idea that all the
numbers $2^{2^{n-1}}+1$ yield a series of prime numbers cannot hold up, as
you already demonstrated, Sir; but it should still be remarkable if this
series were composed only of numbers that could be split into two squares in
a unique way. I should like to risk another conjecture of that kind: any number
composed from two primes is the sum of as many prime numbers (including $1$) as one wishes, right down to the sum that consists just of ones.

After reading this through again, I see that the conjecture can be proved
quite rigorously for the case $n+1$ if it holds for the case $n$ and
$n+1$ can be split into two prime numbers. The proof is very easy;
and at least it appears to be true that every number greater than
$2$ is the sum of three prime numbers."

The translation was done by Martin Mattmüller.