Hi Gabriel, thanks for your invaluable help...
I will review again the process considering your comments. Meanwhile I attach the sample application (just a hello world app) and the public/private key pair.
-----BEGIN RSA PRIVATE KEY-----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-----END RSA PRIVATE KEY-----
-----BEGIN RSA PUBLIC KEY-----
MIIBCgKCAQEAx6ldhzQd1lPG+QrWzw14aOSgEEP/PnhTp7m9Ito3lBSPtwslH9Qm
2awTz9zGHtMpceXMk4wY3/DVCiBQBep3tYGSEt49FnmkFKkCPx5kURTLDfw7/wgd
Bqp8CmogRjYhBXFaExE+HfOgxy1115aOlBuCLkL6mUbI3So5Fifr+DTw1x6eQzA4
m/7VlXHrLLb2cRXSueTQmhCfMLQjv9OM04bzdZ8JNcnnlCKtAPLWcP4FzjTwW7dX
4n5v5mFTPjP+rpKg2TaTfj1h8pKW76W7PAzoa7sG5Hzd57vOpKr7aALOkkqtqkMg
ldrWrS9sS6+Yyeg6X4H+RvLeSHp05Hex3wIDAQAB
-----END RSA PUBLIC KEY-----
Just for clarifying, I'm always using the same version (firstly 3.5.4 and lately 3.6) for both instances so they should be completely compatible for the test. On the other hand, both of them are running under a reverse proxy with nginx, but I think this is not relevant since there are no errors about URLs and everything seems to run right apart from the key validation which is executed locally in the target instance.
Thank you again. Best regards.
PS: I cannot attach the .rei3 file, the uploader is complaining about the extension. I have uploaded it to a github repo.