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I think you've grossly miscalculated something. 2TB is a *shitload* of data. On the fastest available domestic broadband package, that'll take about 19 days to upload. It'll take about five hours on a completely saturated gigabit ethernet connection, assuming that your storage media can sustain 118MB/s reads. There's also the matter of where all that data will go.
AWS Disk Import is an option, although you'll pay about £60 for the privilege. You'll also pay about £33/mo in S3 storage fees and £64/TB in transfer charges. Backblaze B2 offer considerably lower storage and transfer fees, but they charge a small fortune for hard drive ingest.
If you're sending your porn collection to a mate, I'd just post them a hard drive.