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How can I export a canvas with texts and forms from AE to AI?
Other than copy & pasting paths from AE to AI there is no export feature. Otherwise you may use the commercial Lottie script to export an SVG, which of course can be opened in AI.
After Effects creates pixels. You can copy and paste vector paths, not parametric shapes, to Illustrator, but there is no vector export. You can create layered PSD files that can be imported into AI, but that's about it.