Thank you Vladimir,
This was helpful. I made a few changes and here is the final result that works great:
NSArray *paths = NSSearchPathForDirectoriesInDomains(NSDocumentDirectory, NSUserDomainMask, YES);
NSString *documentsDirectory = [paths objectAtIndex:0];
NSString *databasePath = @"personalLMS.s3db";
NSFileManager *fileManager = [[NSFileManager defaultManager] autorelease];
NSString * databasePathFromApp = [[NSBundle mainBundle] pathForResource:@"personalLMS" ofType:@"s3db"];
[fileManager copyItemAtPath:databasePathFromApp toPath:[documentsDirectory stringByAppendingPathComponent:databasePath] error:nil];