He can make his own private key derived from public-key of sender.
No, he cannot. At least unless the crypto (or implementation thereof) is horrifyingly bad in some way.
Public key cryptography as used today is generally based on one of two mathematical problems. For example RSA relies on the difficulty of factoring the product of two large prime numbers (select two primes p and q, calculate and publish n = pq but keep p and q secret; then, given n, find p and q to match), and for example ElGamal relies on the discrete logarithm problem (select b, k and n, calculate g = b^k mod n, publish b, g and n but keep k secret; then given b, g and n, find k to match).
There is a lot more than this to practical and secure public key cryptography, but those are the problems generally relied on to provide confidentiality of the private key. (Confidentiality of the private key, in turn, allows making guarantees about such things as confidentiality and non-repudiation of data.)
If the numbers involved are sufficiently large, there is no currently publicly known, practical way to solve these problems in reasonable amounts of time. They function as a sort of trap door: it's easy to do the calculation in one direction, but impossible in practice to reverse the calculation.
If it becomes possible to solve these types of problems in reasonable amounts of time, then many of our current real-world public-key-based cryptosystems fall apart. There is concern that, if they turn out to be practical, quantum computers could allow quick breaking of many of our current real-world public-key cryptosystems; as a result, there is currently discussion in the cryptographic community on what has been termed post-quantum cryptography.
Note that the above applies only to public-key (asymmetric, different keys used for encryption and decryption) cryptography. Private-key (symmetric, a single key used for both encryption and decryption) cryptography, such as DES or AES, generally does not rely on either integer factorization or the discrete logarithm problem for their security, and as such are not affected by this. There are some issues with symmetric encryption algorithms as well, but those are fairly easily mitigated simply by doubling the key length or hash output length.