Naturalization may be years away, but records are much easier to preserve now than reconstruct later. An asylee should maintain a permanent immigration archive plus ongoing travel, address, and filing histories.
Preserve the full status chain
Keep asylum application records, the asylum approval or court decision, I-94 and identity records, employment authorization documents, travel documents, and later permanent-resident records. When you file Form I-485, keep the complete filed copy, receipt notices, responses, and green-card approval records.
Maintain a travel log
For every trip outside the United States, record departure and return dates, countries visited, purpose, and the passport/travel document used. Keep copies of relevant passport pages, travel documents, tickets or itineraries when useful, and entry records.
Do not rely on memory to reconstruct years of travel later.
Maintain address and employment histories
Keep a chronological list of U.S. addresses and employment/school periods. Update it when you move rather than years afterward.
Preserve records of legal issues
If there is an arrest, citation, charge, court case, immigration issue, or other event that might later need disclosure, preserve the official records and disposition. Do not decide on your own that an old matter is too minor to keep.
Keep tax and family records organized
Future naturalization questions can involve marital history, children, taxes, and other background information. Preserve official records rather than depending on a single online account remaining accessible indefinitely.
Check the rules when the time comes
Eligibility and required evidence depend on the law and your circumstances at the time of filing. Years from now, use the then-current Form N-400 instructions and consider legal review if your history contains complications.
Official sources
This is long-term recordkeeping guidance, not legal advice.