port mapping with fake ip

Hi there, i have a question to all.

The task is:
Redirect port from local host to remote (datapipe etc.) with faking my ip.
For example, nmap with -S option make fake ip of host it being running.
pic:

[my host] -> [remote host]
10.1.1.1:80 10.1.1.130:80
identify as 10.1.1.34

main task - in logs of 10.1.1.130 i was surfing from 10.1.1.134, but really i was 10.1.1.1

It is possible to make such thing using smth tool(s) ? Or it will be easier to write one ?

I am not sure what is the purpose of this question, nor if you are going to use it in a legal way.
To change a local port to be coming from another IP - this is called tunelling. It is quite simple.
If you want to make this on some local machine then you need to mangle with the TCP/IP. There are multiple ways to achieve that. I would suggest Linux + IPTables + SNAT (Source NAT) which is exactly what you need. You might use google to find how to do a SourceNAT (SNAT) on other platforms and using some specific tools.

Short description of what SNAT might be:
"If a packet is going out from my PC from port 1234 then its source IP should be replaced to IP 5.6.7.8". It would be something like (might be wrong as I am not testing that): "iptables -A MANGLE -p tcp --sport 1234 -j SNAT --from-ip 5.6.7.8"