It stopped ringing just as I was about to pick it up.
I was just about to pick it up, when the phone stopped ringing.
ご質問ありがとうございます。
①
"It stopped ringing"＝「それ（電話）は鳴りやんだ」
"just as I was about to"＝「ちょうど私が～をするときに」
"pick it up."＝「（電話）にでるときに。」
②
"I was just about to pick it up"＝「私はちょうどそれに出るところだった」
"when the phone stopped ringing."＝「電話が鳴りやんだときに。」
ご参考になると良いです！
アメリカ合衆国 
