curl --request POST \
  --url https://api.lemlist.com/api/inbox/email \
  --header 'Authorization: Basic <encoded-value>' \
  --header 'Content-Type: application/json' \
  --data '
{
  "sendUserId": "usr_FU6yAd3UdBFel0UDy",
  "sendUserEmail": "john@example.com",
  "sendUserMailboxId": "usm_pmZsNNO1gl5nwCQ07",
  "message": "<p>Hello,</p><p>Following up on our conversation...</p>"
}
'

import requests

url = "https://api.lemlist.com/api/inbox/email"

payload = {
    "sendUserId": "usr_FU6yAd3UdBFel0UDy",
    "sendUserEmail": "john@example.com",
    "sendUserMailboxId": "usm_pmZsNNO1gl5nwCQ07",
    "message": "<p>Hello,</p><p>Following up on our conversation...</p>"
}
headers = {
    "Authorization": "Basic <encoded-value>",
    "Content-Type": "application/json"
}

response = requests.post(url, json=payload, headers=headers)

print(response.text)

const options = {
  method: 'POST',
  headers: {Authorization: 'Basic <encoded-value>', 'Content-Type': 'application/json'},
  body: JSON.stringify({
    sendUserId: 'usr_FU6yAd3UdBFel0UDy',
    sendUserEmail: 'john@example.com',
    sendUserMailboxId: 'usm_pmZsNNO1gl5nwCQ07',
    message: '<p>Hello,</p><p>Following up on our conversation...</p>'
  })
};

fetch('https://api.lemlist.com/api/inbox/email', options)
  .then(res => res.json())
  .then(res => console.log(res))
  .catch(err => console.error(err));

require 'uri'
require 'net/http'

url = URI("https://api.lemlist.com/api/inbox/email")

http = Net::HTTP.new(url.host, url.port)
http.use_ssl = true

request = Net::HTTP::Post.new(url)
request["Authorization"] = 'Basic <encoded-value>'
request["Content-Type"] = 'application/json'
request.body = "{\n  \"sendUserId\": \"usr_FU6yAd3UdBFel0UDy\",\n  \"sendUserEmail\": \"john@example.com\",\n  \"sendUserMailboxId\": \"usm_pmZsNNO1gl5nwCQ07\",\n  \"message\": \"<p>Hello,</p><p>Following up on our conversation...</p>\"\n}"

response = http.request(request)
puts response.read_body

<?php

$curl = curl_init();

curl_setopt_array($curl, [
  CURLOPT_URL => "https://api.lemlist.com/api/inbox/email",
  CURLOPT_RETURNTRANSFER => true,
  CURLOPT_ENCODING => "",
  CURLOPT_MAXREDIRS => 10,
  CURLOPT_TIMEOUT => 30,
  CURLOPT_HTTP_VERSION => CURL_HTTP_VERSION_1_1,
  CURLOPT_CUSTOMREQUEST => "POST",
  CURLOPT_POSTFIELDS => json_encode([
    'sendUserId' => 'usr_FU6yAd3UdBFel0UDy',
    'sendUserEmail' => 'john@example.com',
    'sendUserMailboxId' => 'usm_pmZsNNO1gl5nwCQ07',
    'message' => '<p>Hello,</p><p>Following up on our conversation...</p>'
  ]),
  CURLOPT_HTTPHEADER => [
    "Authorization: Basic <encoded-value>",
    "Content-Type: application/json"
  ],
]);

$response = curl_exec($curl);
$err = curl_error($curl);

curl_close($curl);

if ($err) {
  echo "cURL Error #:" . $err;
} else {
  echo $response;
}

{
  "ok": true,
  "contactId": "ctc_JgrwGbHKgFoEnunBA"
}

Bad team

The authentication you supplied is incorrect