you should collect the header field in the first response and reuse them in the next request
there are two methods for that:
void addHeader(const String& name, const String& value, bool first = false, bool replace = true);
/// Response handling
void collectHeaders(const char* headerKeys[], const size_t headerKeysCount);
I've never done this on a client, but this might give a first idea
const char* headers[] = {"Set-Cookie"};
client.collectHeaders(headers, sizeof(headers)/ sizeof(headers[0]));
parse the content and extract the information from headers.
add the information based on the wikipedia example to the next request:
client.addHeader("Cookie", "content");