تحرر هذا العقد لدى الأستاذ الموثق لدى ولاية " " بالجزائر قيد حياته اختصاص محكمة الجزائر المؤرخ في:
The contract is notarized by the authorized notary public in the state of [state name] in Algeria, while the individual is alive, and falls under the jurisdiction of the Algerian Court. The contract is dated [date].

Other options:
while the individual is alive:
- during the person's lifetime
- throughout the person's life
- as long as the person is alive
- during the person's existence
- during the person's lifespan

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Note added at 21 mins (2023-07-03 17:36:29 GMT)
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I prefer the following translation:
in his lifetime

in (one's) lifetime (redirected from in his lifetime)

in (one's) lifetime
During one's life; before one dies.
https://idioms.thefreedictionary.com/in his lifetime

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